FORT  DEARBORN  HOTEL,  CHICAGO 
Holabird  &  Roche,  Architects 


STEEL  CONSTRUCTION 


A  TEXT  AND  REFERENCE  BOOK  COVERING 
THE  DESIGN  OF  STEEL  FRAME- 
WORK FOR  BUILDINGS 


By  HENRY  JACKSON  BURT,  C.E. 

MEMBER   AMERICAN    SOCIETY    OP  CIVIL    ENGINEERS 

MEMBER   WESTERN    SOCIETY    OF   ENGINEERS 

MEMBER   SOCIETY   FOR  THE    PROMOTION    OF   ENGINEERING   EDUCATION 
STRUCTURAL   ENGINEER   FOR   HOLABIRD   AND   ROCHE,    ARCHITECTS 


ILLUSTRATED 


AMERICAN  TECHNICAL  SOCIETY 

CHICAGO 

1914 


I 


COPYRIGHT,  .1914,    BY 

AMERICAN  TECHNICAL  SOCIETY 


COPYRIGHTED  IX  GREAT  BRITAIN 
ALL  BIGHTS   RESERVED 


CONTENTS 


PAGE 

Introduction 1 

Method  of  manufacture 9 

Steel  sections — adaptability  and  use 23 

Properties  of  sections 35 

General  information 40 

Quality  of  material 42 

Standard  specifications 42 

Discussion  of  important  features 44 

Unit  stresses 49 

Rivets  and  bolts 52 

Beams 75 

Review  of  theory  of  beam  design 76 

Calculation  of  load  effects 80 

Calculation  of  resistance 97 

Practical  applications 113 

Details  of  construction 120 

Riveted  girders 134 

Theory  of  design 135 

Design  of  plate  girder 137 

Other  forms  of  riveted  girders « . . . .  158 

Practical  applications 162 

Details  of  construction • 165 

Compression  members — columns 173 

Steel  columns 173 

Loads  and  their  effects 173 

Strength  of  columns — formulas 179 

Column  sections * 181 

Tables 188 

Details  of  construction 216 

Cast-iron  columns 225 

Characteristics 225 

Strength — formula 228 


CONTENTS 

PAGE 

Compression  members — columns 
Cast-iron  columns 

Tables 230 

Details  of  construction 232 

Tension  members 233 

Loads  and  their  effects 233 

Sections 235 

Details  of  connections 23? 

Wind  bracing 239 

General  conditions 239 

Systems  of  framework , . .  243 

Design  of  wind-bracing  girders 255 

Combined  wind  and  gravity  stresses  in  girders .262 

Effect  of  wind  stresses  on  columns , 266 

Practical  design — a  sixteen-story  fireproof  hotel 269 

Fireproof  specifications 294 

Loads 295 

Type  of  floor  construction 301 

Framing  specifications 306 

Design  of  steel  members 309 

Column  pedestals 319 

Wind  bracing 322 

Miscellaneous  features 327 

Dimensioning  drawings 329 

Protection  of  steel 333 

Protection  from  rust 333 

Rust  formation 333 

Paint 335 

Protection  from  fire -. 339 

Specifications , 349 

General  characteristics 350 

Example  of  specifications 353 

Index...  ..373 


INTRODUCTION 

A  GREAT  part  of  the  satisfaction  derived  from  the  practice 
of  engineering  comes  from  seeing  the  "dreams  come  true". 
The  engineer  is  commonly  assumed  to  deal  with  facts  and  to  be 
guided  by  mathematical  relations.  While  this  is  true,  he  must  at 
times  be  a  dreamer,  a  man  with  an  active  imagination.  Before  a  line 
is  drawn  or  a  figure  placed  on  paper,  the  engineer  must  have  some 
conception  of  the  structure  he  is  to  create.  The  more  definite 
this  conception,  the  more  readily  it  can  be  committed  to  paper 
in  the  form  of  drawings.  The  mention  of  a  building  of  a  certain 
dze  or  for  a  certain  purpose  brings  a  vision  of  the  skeleton  to 
support  it;  the  architect's  perspective  or  elevation  suggests  the 
columns  concealed  within  the  piers  and  the  girders  behind  the 
spandrels;  the  floor  plans  indicate  the  location  of  columns,  girders, 
and  joists  which  will  be  required  to  support  the  floors,  partitions, 
and  walls.  From  these  mental  pictures,  the  design  drawings 
can  be  evolved  by  applying  the  mathematical  relations  to  deter- 
mine the  sizes  of  members  required. 

<!  But  the  use  of  the  imagination  does  not  stop  here;  it  is  needed 
in  perfecting  the  details.  The  more  fully  it^is  developed,  the 
more  quickly  can  proper  sizes  and  arrangement  of  material  be 
established.  Imagination  is  a  natural  talent  which  can  be  im- 
proved by  practice  and  experience.  It  is  not  easily  distinguished 
from  the  judgment  resulting  from  experience. 

^  This  book  does  not  deal  with  the  visions  of  proposed  struc- 
tures, but  with  the  facts  and  formulas  for  transforming  these 
visions  into  tangible  designs.  Haying  realized  the  dream  in 
definite  plans,  there  follows  the  growth  of  the  practicable  struc- 
ture. The  successful  completion  of  the  skeleton  which,  silently 


INTRODUCTION 

and  unseen,  must  carry  the  weight  of  the  building  with  assurance 
of  perfect  safety  to  the  people  who  occupy  it,  must  give  great 
satisfaction  to  him  whose  brain  has  created  it.  Then  has  the 
"dream  come  true". 

<I  This  book  is  intended  to  give  its  students  the  facts  and  formulas 
needed  in  designing  the  structural  steel  framework  for  buildings. 
Since  facts  and  formulas  alone  would  be  of  little  use,  they  are 
accompanied  by  explanations  of  the  underlying  principles,  a 
clear  understanding  of  which  is  essential  to  the  intelligent  use 
of  the  formulas.  The  use  of  the  formulas  is  shown  by  illus- 
trations of  a  practical  nature  which  serve  not  only  to  teach  the 
proper  application,  but  to  illustrate  current  practice  in  this  form 
of  construction. 

<I  For  use  as  a  textbook  by  students,  the  important  feature  is 
the  theory  on  which  are  based  the  formulas  and  their  applications. 
A  student  can  easily  learn  to  use  tables,  apply  formulas,  and  copy 
the  work  of  others.  But  without  a  knowledge  of  the  fundamental 
principles  he  will  not  be  able  to  determine  the  proper  limitations 
of  the  tables  and  formulas  nor  to  distinguish  the  good  and  bad 
features  of  designs  made  by  himself  or  others. 

^f  For  use  as  a  reference  by  designers,  the  book  brings  together 
the  necessary  data,  easily  accessible,  for  the  complete  design  of 
structural  steel  work  for  business  buildings,  and  gives  enough 
illustrations  to  guide  in  the  solution  of  the  problems  usually 
encountered  in  practice.  A  unique  feature  of  this  book  is  a 
complete  set  of  drawings  and  detailed  explanations  in  connection 
with  the  design  of  a  sixteen-story  hotel.  This  study  alone  cannot 
help  but  be  of  immense  benefit  to  those  who  are  interested  in 
the  design  end  of  this  most  important  subject. 


•ill    in.,    iiti    «p 

lot  ta  is 


FXIVERSITY  CLUB,  CHICAGO 
Holabird  &  Roche,  Architects 


MONROE  BUILDING,  CHICAGO 
Holabird  &  Roche,  Architects 


CONSTRUCTION 


PART  I 
INTRODUCTION 

Scope  of  Work.  The  subject  of  steel  construction  as  here  used 
covers  the  use  of  structural  steel  for  the  supports  for  buildings, 
whether  in  the  forms  of  isolated  members  or  complete  framework. 
It  deals  especially  with  architectural  structures,  such  as  business 
buildings,  office  buildings,  warehouses,  residences,  etc.  Mill  build- 
ings and  roof  trusses  might  properly  be  included  Under  this  subject, 

a  they  are  not  absolutely  essential  to  the  present  discussion, 
their  treatment  has  been  omitted. 

Consideration  is  given  first  to  the  structural  steel  sections,  i.  e., 
the  shapes  in  which  the  material  is  available,  such  as  plates,  angles, 
I-beams,  etc.,  studying  their  properties  and  uses.  Certain  definite 
riizes,  shapes,  and  weights  of  sections  can  be  purchased  in  the  mar- 
ket. Acquaintance  with  these  sections  and  some  knowledge  of  the 
purposes  for  which  the  special  shapes  are  adapted  are  essential 
preliminaries  to  the  study  of  steel  design. 

The  designer  should  know  the  quality  of  the  material  which  he 
is  using;  therefore,  a  brief  discussion  of  the  chemical  composition 
and  physical  properties  of  steel  for  structural  purposes  is  given. 

Experience  and  experiment  have  established  the  working  loads, 
i.  e.,  unit  stresses,  that  can  be  applied  safely  to  structural  steel  under 
various  conditions.  The  values  now  used  are  so  well  established 
that  they  may  be  considered  as  standard.  Consequently,  the  unit 
stresses  are  given  with  only  such  discussion  as  is  necessary  to  explain 
their  application. 

After  these  preliminary  considerations  comes  the  study  of 
design.  As  rivets  and  bolts  are  used  in  all  forms  of  structural 
members,  a  section  of  the  text  is  devoted  to  them  before  taking  up 
beams,  columns,  and  tension  members.  The  study  of  these  mem- 


2  STEEL  CONSTRUCTION 

bers  give?  a  T-view  of  the  theory  involved,  the  formulas,  the  compu- 
tation of  loads,  the  application  to  assumed  cases,  and  details  of 
construction. 

Having  studied  the  elements  of  the  structure  as  described 
above,  complete  structures  are  then  investigated  and  designed. 
Examples  of  existing  structures  are  taken  for  this  purpose.  And, 
finally,  there  is  a  discussion  of  painting,  fireproofing,  and  speci- 
fications. 

Structural  steel  is  a  perishable  material  if  exposed  to  the  ele- 
ments and  is  so  to  a  considerable  extent  when  enclosed  in  a  building 
but  exposed  freely  to  the  air.  It  is  a  dangerous  material  when 
exposed  to  fire.  A  part  of  the  designer's  duty  is  to  provide  the 
necessary  protection  from  corrosion  and  from  fire;  consequently, 
considerable  attention  is  given  to  painting  and  fireproofing. 

The  specifications  for  structural  steel  are  quite  well  standard- 
ized so  far  as  usual  provisions  are  concerned.  Nevertheless,  some 
modifications  or  additions  are  usually  required  for  each  job.  The 
requirements  are  outlined  briefly  in  the  text. 

Purpose.  It  is  the  purpose  of  this  book  to  give  a  thorough 
presentation  of  the  theory  and  practice  of  design.  It  is  believed 
that  careful  study  of  the  text  and  faithful  work  in  solving  the  prob- 
lems will  furnish  the  proper  equipment  for  designing  any  ordinary 
steel  construction.  The  ability  to  deal  with  complicated  problems 
will  follow  naturally  after  practice  with  the  simpler  ones. 

In  addition  to  its  uses  as  a  textbook,  this  work  is  suitable  for  a 
reference  book  for  designers,  being  especially  useful  to  those  who 
have  to  design  steel  work  only  occasionally,  and  to  beginners  in 
practical  work.  It  does  not  pretend  to  offer  anything  new,  but 
aims  to  explain  in  a  simple  Way  the  established  theory  and 
practice, 

Preparation.  Fundamental  Principles.  In  order  to  take  up 
the  design  of  structural  steel  work,  it  is  necessary  that  one  have  an 
understanding  of  the  theory  and  the  formulas  used  in  the  design 
of  the  steel  members.  It  is  assumed  that  the  essential  parts  of  the 
theory,  as  referred  to  in  "Strength  of  Materials",  "Structural 
Drafting",  "Statics",  and  "Roof  Trusses",  have  been  mastered, 
and  if  this  is  not  true,  these  subjects  should  be  reviewed  before 
proceeding  with  "Steel  Construction*'. 


STEEL  CONSTRUCTION  3 

It  is  of  the  greatest  importance  that  the  fundamental  principles, 
that  is,  the  theory  underlying  the  operations  in  designing,  be  kept 
in  mind.  Only  in  this  way  can  one  be  sure  that  no  step  in  the  work 
has  been  omitted.  This  understanding  of  the  theory  will, 'in  a  large 
measure,  remove  the  necessity  for  formulas.  It  would  be  impossible 
to  illustrate  all  the  problems  that  come  up  in  actual  practice,  so  that 
the  designer  must  understand  the  theory  in  order  to  design  with 
reasonable  assurance  of  correctness  and  to  solve  the  innumerable 
problems  that  arise. 

Simple  Mathematical  Requirements.  The  mathematics  required, 
in  designing  are  little  more  than  arithmetic.  It  is  true  that  the', 
formulas  are  expressed  in  algebraic  terms,  but  as  these  formulas 
are  in  the  form  required  for  direct  application  to  the  problems,  no 
algebraic  transformations  are 
necessary  in  ordinary  cases.  The 
work  to  be  done  simply  consists 
in  substituting  numerical  values 
for  the  letters  and  performing 
the  additions,  subtractions,  mul- 
tiplications, and  divisions  indi-  ywo  |5«? 
cated  by  the  symbols.  The 
formulas  will  be  stated  in  wrords 
as  well  as  in  letters  so  that  the 
designer  need  not  follow  set  eso\  (b) 

examples.  Fig.  1.     Diagram    Showing    Forces   in 

Equilibrium 

Equilibrium  Relations.  The 

three  fundamental  relations  of  equilibrium,  illustrated  in  Fig.  1, 
must  always  be  kept  in  mind,  viz: 

(1)  Summation  of  horizontal  forces  equals  zero 

(2)  Summation  of  vertical  forces  equals  zero 

(3)  Summation  of  moments  equals  zero 

In  the  textbook  on  "Statics,"  equilibrium  is  defined  as  follows: 
When  a  number  of  forces  act  upon  a  body  which  is  at  rest,  each  tends 
to  move  it;  but  the  effects  of  all  the  forces  acting  upon  that  body  may 
counteract  or  neutralize  one  another,  and  the  forces  are  said  to  be  bal- 
anced or  in  equilibrium. 

Fig.  1-a  represents  a  body  to  which  certain  forces  are  applied. 
The  horizontal  forces  h  and  h'  are  equal  and  opposite  in  direction, 


fQ,  Q,, 


4  STEEL  CONSTRUCTION 

thus  satisfying  the  first  relation.  Likewise  the  vertical  forces  satisfy 
the  second  relation.  The  horizontal  forces  are  in  the  same  straight 
line  and  the  vertical  forces  are  in  one  straight  line,  hence  there  is 
no  tendency  to  rotate  and  the  third  relation  is  satisfied.  All  of  this 
is  evident  from  the  drawing. 

Fig.  1-b  represents  a  more  complicated  case.  There  are  no 
horizontal  forces.  The  vertical  forces  acting  downward  are  1000 
+500  =  1500;  acting  upward  are  850+650=1500;  hence  the  sum- 
mation equals  zero.  Taking  any  point  o  as  a  center,  the  moments 
clockwise  are 

5X1000  =  5000 
9X  500  =  4500 

9500 

The  moments  in  the  opposite  direction  are 
2X    850  =  1700 
12X    650=7800 

9500 

Hence  the  summation  of  moments  equals  zero,  and  the  forces 
acting  on  the  body  are  in  equilibrium. 

It  is  because  it  is  essential  that  these  relations  be  mastered 
that  they  are  stated  here.  They  will  be  referred  to  frequently 
throughout  the  work  on  designing. 

Method  of  Presentation.  Throughout  the  discussion  relating  to 
the  design  of  structural  steel  members,  the  order  of  presentation  is 

(a)  Review  of  Theory 

(b)  Calculation  of  Loads 

(c)  Calculation  of  Resistance 

(d)  Practical  Application 

(e)  Details  of  Construction 

Review  of  Theory.  Although  it  has  been  assumed  that  the 
student  has  had  some  training  in  the  theory  of  design,  this  subject 
is  briefly  reviewed. 

Cdlcjdaiion  of  Loads.  The  calculation  of  loads  on  steel  mem- 
bers is  usually  the  most  laborious  part  of  designing.  This  work  has 
to  be  done  in  each  individual  case,  as  it  is  not  possible  to  standard- 
ize the  loads  which  are  applied  to  structures.  Accurate  data  as  to 
the  weights  of  the  materials  of  construction  which  must  be  sup- 


STEEL  CONSTRUCTION  5 

ported  by  the  steel  framework  are  not  always  available;  in  fact, 
the  weights  of  certain  materials,  as  furnished  by  different  manu- 
facturers, vary  considerably.  The  live,  or  imposed,  loads  must 
generally  be  assumed  or  approximated  from  prospective  conditions 
of  use  which  may  be  more  or  less  uncertain.  Consequently,  this 
branch  of  the  study  involves  not  only  careful  computation,  but  the 
exercise  of  judgment 

Calculation  of  Resistance.  The  calculation  of  resistance  of  steel 
members  to  the  loads  applied  is  also  a  laborious  matter  when  a  start 
must  be  made  from  the  beginning,  but  the  steel  construction  has 
been  so  standardized  that  the  number  of  sizes  of  material  used  is 
relatively  small.  Tables  are  available,  giving  the  properties  and 
resistance  factors  of  these  sections,  so  that  it  is  usually  an  easy 
matter  to  design  the  section  required  for  a  given  situation  after  the 
loads  have  been  computed.  This  statement  does  not  apply  very 
generally  to  built-up  sections  such  as  plate  girders  and  columns,  as 
these  members  have  been  standardized  only  to  a  limited  extent. 
Consequently,  it  is  necessary  for  the  designer  to  be  able  to  compute 
the  resistance  of  the  member,  having  given  only  its  dimensions  and 
the  permissible  unit  loads.  Even  in  the  case  of  I-beams  there  are 
many  cases  where  the  work  must  go  back  to  the  fundamental  rela- 
tions; as,  for  example,  in  cases  where  holes  are  punched  in  the 
tension  flange  of  a  beam  at  the  point  of  maximum  bending  moment, 
or  where  a  portion  of  the  flange  is  cut  away 

Practical  Application.  Numerous  examples  arc  worked  out  to 
illustrate  the  principles  and  methods  covered  by  the  text,  and 
similar  problems  are  submitted  for  solution.  The  examples  and 
problems  are  taken  from  actual  construction  work,  as  it  is  believed 
that  they  are  more  useful  and  interesting  than  abstract  illustrations. 

Details  of  Construction.  This  section  of  the  work  explains  the 
usual  methods  used  in  detailing  the  connections  of  steel  members 
to  each  other  and  is  illustrated  by  numerous  drawings. 

Reference  Books.  Tables  giving  the  properties  of  steel  sec- 
tions and  data  giving  the  strength  of  steel  members  are  given  in  the 
handbooks  published  by  the  steel  manufacturers.  These  books  are 
so  convenient  for  reference  and  so  easily  obtainable  that  no  attempt 
is  made  to  repeat  in  this  text  the  tables  and  data  given  in  them,  the 
supposition  being  that  the  reader  either  has  one  or  will  provide 


6  STEEL  CONSTRUCTION 

himself  with  one  of  these  handbooks.  References  are  repeatedly 
made  to  the  handbooks  and,  as  far  as  practicable,  are  made  in 
general  terms,  so  that  any  one  of  the  reference  books  may  be  used. 
This  is  an  important  point,  as  these  reference  books  are  being  revised 
from  time  to  time  and  the  one  in  use  at  the  present  time  might 
be  supplanted  in  a  year  or  two  by  one  of  another  manufacturer 
which  is  more  up-to-date.  Handbooks  are  published  by  The  Cam- 
bria Steel  Company,  Johnstown,  Pa.;  Carnegie  Steel  Company, 
Pittsburgh,  Pa.;  Jones  and  Laughlins,  Pittsburgh,  Pa.;  and  Bethle- 
hem Steel  Company,  South  Bethlehem,  Pa. 

In  addition  to  the  handbooks  there  are  a  number  of  other 
reference  books  available  for  special  purposes  that  can  be  purchased 
through  the  book  stores.  They  are  not  essential  for  this  study,  but 
are  of  considerable  use  to  designers.  They  will  be  referred  to  in 
the  text  in  connection  with  the  special  features  to  which  they  relate. 

Tables.  The  tables  given  in  reference  books  are  generally 
reliable;  nevertheless,  errors  do  occur  in  them  and  it  is  prudent  to 
check  them  with  the  formulas  sufficiently  to. make  sure  that  they 
are  computed  on  a  correct  basis,  or  that  the  user  understands  the 
basis  on  which  they  are  computed.  As  an  illustration  of  the  latter 
point,  attention"  is  called  to  the  fact  that  some  tables  of  strength 
are  stated  in  tons  and  others  in  thousands  of  pounds.  Of  course  the 
heading  of  the  table  should  show  this,  but  special  care  should  be 
taken  to  make  sure  which  is  used.  A  designer  may  be  using  a  table 
for  beams  given  in  tons  and  a  table  for  columns  given  in  thousands  of 
pounds,  in  which  case  it  would  be  very  easy  to  get  columns  designed 
only  half  strong  enough  or  beams  with  twice  the  necessary  strength. 
Similarly,  there  is  a  chance  for  confusion  between  moments  expressed 
in  foot-pounds  and  moments  expressed  in  inch-pounds.  Also  there 
is  a  chance  for  error  in  using  the  weight  per  lineal  foot  of  a  section 
when  it  is  intended  to  use  the  cross-sectional  area,  or  vice  versa. 
This  matter  is  given  further  consideration  later. 

PROBLEM 

Refer  to  the  handbook  and  make  a  list  of  all  the  tables  therein  in 
which  the  strength  is  given  in  tons,  and  another  list  in  which  the  strength  is 
given  in  pounds  or  thousands  of  pounds. 

If  the  handbook  has  been  well  edited,  all  tables  will  have  the 
same  basis.  Make  a  careful  search  of  the  book  to  ascertain  definitely 


STEEL  CONSTRUCTION  7 

its  make-up  in  this   relation.     When  there  is  occasion  to  use  a 
different  handbook,  investigate  immediately  in  the  same  manner. 

PROBLEM 

Refer  to  the  handbook  for  all  references  and  tables  relating  to  moments. 
Make  a  list  of  all  cases  where  moments  are  expressed  in  foot-pounds  and  another 
list  of  cases  where  they  are  expressed  in  inch-pounds. 

Note  that  moments  of  inertia  are  always  expressed  in  inches, 
so  that  in  all  cases  where  the  moments  of  inertia  of  sections  are  used 
in  computations,  the  bending  moment  must  be  expressed  in  inch- 
pounds.  On  the  other  hand,  the  resisting  moments  of  beams  are 
usually  given  in  foot-pounds,  and  the  bending  moments  must  be 
computed  in  the. same  units 

PROBLEM 

Select  at  random  from  the  handbook  twenty  or  more  different  sizes  of 
angles,  I-beams,  plates,  etc.,  and  set  down  in  parallel  columns  the  area  in  square 
mches  and  the  weight  per  lineal  foot  of  each  item. 

Note  that  in  each  case  the  weight  is  3.4  times  the  area.    That 
is,  a  piece  of  steel  having  a  cross-sectional  area  of  one  square  inch 
weighs  3.4  pounds  per  lineal  foot. 
PROBLEM 

What  is  the  weight  of  one  cubic  foot  of  steel?    Of  one  cubic  inch  of  steel?. 

Factor  of  Safety.  Older  works  and  specifications  dealing  with 
steel  construction  frequently  use  the  expression  "factor  of  safety." 
It  is  used  to  express  the  ratio  of  the  ultimate  strength  of  the  material 
to  the  safe  working  strength.  In  steel  construction,  this  ratio  is 
commonly  stated  to  be^4,  being  based  on  the  ultimate  strength  of 
64,000  pounds  per  square  inch  and  a  working  strength  of  16,000 
pounds  per  square  inch.  This  expression  is  a  misnomer  and  its  use 
is  to  be  discouraged,  because  it  gives  a  wrong  understanding  of  the 
facts  and  leads  to  an  unwarranted  sense  of  security.  Later  on  in 
this  treatise  it  is  shown  that  the  actual  strength  of  steel  work  under 
loads  continuously  applied  is  only  about  one-half  of  the  ultimate 
strength  of  the  material,  so  that  the  real  factor  of  safety  is  2  where 
the  nominal  factor  of  safety  is  4 

Further  this  expression  has  been  used  unscrupulously  in  argu- 
ments with  owners  to  persuade  them  to  use  lighter  steel  work  than 
standard  practice  permits;  and,  on  the  other  hand,  it  has  been  used 
by  the  owners  themselves  without  realizing  the  true  meaning  of 
the  expression,  in  an  attempt  to  reduce  cost. 


8  STEEL  CONSTRUCTION 

This  expression  is  quite  certain  to  come  up  from  time  to  time 
in  discussions  with  laymen  and  in  such  cases  the  distinction  between 
the  actual  and  the  nominal  factors  of  safety  must  be  made  clear. 

Procedure  in  Furnishing  Structural  Steel.  There  are  three 
steps  in  furnishing  structural  steel:  first,  the  rolling  of  the  plain 
material;  second,  the  fabrication  of  the  plain  material  into  the  con- 
ditions required  for  use;  and  third,  the  erection  of  the  material  in  the 
structure. 

The  work  of  the  rolling  mill  consists  in  rolling  the  steel  sec- 
tions of  the  sizes  and  lengths  as  required  by  the  order.  The 
work  of  the  fabricating  shop  is  to  do  the  punching,  cutting,  assem- 
bling, riveting,  and  painting  of  the  material  as  required  for  use  jn  the 
structure.  The  work  of  the  erector  is  to  place  the  pieces  in  position 
in  the  structure  and 'bolt  or  rivet  them  together.  Some  concerns 
perform  all  three  of  these  steps;  many  perform  only  the  second  and 
third;  and  in  still  other  cases  the  second  and  third  steps  may  be 
performed  by  separate  organizations.  The  owner  may  deal  with  a 
general  contractor  who  undertakes  to  secure  the  performance  of  all 
three  steps;  or  he  may  deal  separately  with  a  fabricating  company 
and  with  an  erection  company.  The  former  undertakes  to  deliver  the 
fabricated  material  ready  for  erection,  purchasing  the  material  from 
the  rolling  mills.  It  is  only  in  very  rare  instances  that  separate  con- 
tracts are  made  for  furnishing  the  plain  material  and  for  fabricating. 

The  design  of  the  structural  steel  work  is  usually  made  by  an 
architect,  or  by  an  engineer  co-operating  with  the  architect.  The 
design  drawings  should  show  all  the  necessary  dimensions  of  the 
structure,  sizes  of  members,  loads  on  the  individual  members,  and 
details  of  connections  other  than  those  considered  as  standard. 
These  drawings  show  the  members  assembled  in  their  proper  rela- 
tions to  each  other.  They  must  also  show  any  connections  required 
for  attaching  or  supporting  other  construction  materials. 

As  a  part  of  the  work  of  fabricating,  working  drawings  must  be 
prepared  by  the  engineering  department  of  the  fabricating  com- 
pany, or  by  other  engineers  employed  by  it.  These  working  draw- 
ings, or  shop  details,  divide  the  work  into  individual  members,  and 
a  complete  drawing  is  made  of  each  member,  showing  all  dimen- 
sions, the  position  of  rivets,  and  the  exact  location  of  the  open  holes 
required  for  connections  with  other  members  of  the  structure. 


STEEL  CONSTRUCTION  9 

STRUCTURAL  STEEL 

METHODS  OF  MANUFACTURE 

The  procedure  in  the  manufacture  of  structural  steel  sections 
from  iron  ore  consists  of  the  following  operations:  (1)  smelting  the 
iron  ore  and  producing  pig  iron;  (2)  converting  the  pig  iron  into 
steel  ingots;  and  (3)  rolling  the  ingots  into  steel  sections. 

Iron  Ore  to  Pig  Iron.  Iron  ore  is  a  chemical  combination  of 
iron  and  oxygen.  It  exists  in  several  forms.  Pure  ore  has  a  maxi- 
mum of  about  70  per  cent  of  iron.  The  ores  as  mined  are  mixed 
with  various  substances,  chiefly  water,  silica,  and  limestone,  with 
small  quantities  of  phosphorus,  sulphur,  titanium,  manganese,  etc., 
so  that  commercial  ore  contains  only  50  per  cent  of  iron,  or  even 
less. 

Process  of  Smelting.-  The  purpose  of  smelting  the  ore  is  to 
break  down  the  chemical  combination  of  iron  and  oxygen,  and  to 
eliminate  the  greater  part  of  the  impurities  from  the  resulting 
metallic  iron.  This  is  accomplished  by  melting  the  ore  in  a  blast 
furnace  The  heat  for  melting  the  ore  is  supplied  by  coke,  and 
the  melting  point  is  brought  to  a  lower  temperature  than  otherwise 
would  be  required  by  mixing  limestone  with  the  ore.  As  the  con- 
tents of  the  furnace  melt,  they  drip  down  to  the  bottom  where  the 
molten  iron  separates  from  the  molten  slag  by  gravity,  the  iron, 
being  heavier,  settling  to  the  bottom. 

A  section  of  a  blast  furnace  and  skip  hoist  is  shown  in  Fig.  2. 
The  skip  or  car  at  the  bottom  of  the  machine  is  loaded  with  ore, 
limestone,  and  coke  from  the  bins;  it  is  then  hauled  up  the  incline 
where  the  material  is  charged  into  the  blast  furnace.  Fig.  3  shows 
a  section  through  the  bottom  part  of  the  furnace,  which  represents 
graphically  the  melting  charge  and  the  accumulation  of  iron 
and  slag  in  separate  layers  at  the  bottom  of  the  furnace.  The  blast 
of  air  required  for  burning  the  coke  is  admitted  through  the  open- 
ings, called  "tuyeres,"  near  the  bottom  of  the  furnace. 

The  operation  of  the  blast  furnace  is  continuous  from  the  time 
it  is  fired  until  it  is  shut  down  for  repairs,  or  for  other  reasons.  As 
the  metal  and  slag  accumulate  at  the  bottom,  they  are  drawn  off, 
the  metal  into  molds  to  form  pigs,  Fig.  4,  and  the  slag  to  the  dump. 
More  material  is  added  at  the  top  of  the  furnace  as  the  contents  melt. 


10  STEEL  CONSTRUCTION 

Pig  Iron.  The  pig  iron  resulting  from  this  operation  contains 
3  or  4  per  cent  of  carbon;  a  small  amount  of  sulphur  which  has  been 
absorbed  from  the  coke;  about  4  per  cent  of  silicon;  and  smaller 
quantities  of  manganese  and  phosphorus  which  remain  from  the  ore. 


Fig.  2.    Cross  Section  of  Blast  Furnace  and  Skip  Hoist 
From  Stoughton's  "Metallurgy  of  Iron  and  Steel" 
Courtesy  McGraw-Hill  Publishing  Company 

The  iron  may  not  be  cast  into  pigs  but  may  be  maintained  in 
a  molten  condition  ready  for  the  next  operation,  if  the  Bessemer 
process  is  used.  In  this  case  it  is  poured  into  a  large  vessel,  called 


STEEL  CONSTRUCTION 


11 


a  "mixer,"  Fig.  5,  which  may  hold  a's  much  as  500  tons.    Heat  can 
be  applied  to  it  if  needed. 

Pig  Iron  to  Steel.    The  change  from  pig  iron  to  steel  consists 
of  the  reduction  of  the  carbon  to  about  0.2  per  cent  and  the  elimina- 


Fusion  Level 


Legend;—  Lumpsof  Coke ^ 

Lumps  of  Iron  Ore & 

Lumps  of  Lime .Q 

Drops  of  Slag ___() 

Drops  of  Iron / 

La/er  of  Molten  Slag 

Layer  of  Molten  Iron 


Fig.  3. 


Section  Through  Base  of  Furnace  Showing  Layers  of  Molten  Iron  and 

Slag  with  Unmelted  Ingredients  Above 

From  Stoughton's  "Metallurgy  of  Iron  and  Steel 

Courtesy  McGraw-Hill  Publishing  Company 


tion  of  impurities  as  fully  as  possible.  There  are  two  processes  of 
doing  this,  the  Bessemer  and  the  Open  Hearth.  They  are  described 
in  "Metallurgy  of  Iron  and  Steel"*  as  follows: 

*By  Bradley  Stoughton,  Copyright  1913.  McGraw-Hill  Publishing  Company. 


Fig.  4.     Pig  Beds 

From  Stough ton's  "Metallurgy  of  Iron  and  Steel" 
Courtesy,  McGraw-Hill  Publishing  Company 


STEEL  CONSTRUCTION 


13 


"Bessemer  Process.  In  the  Bessemer  process,  perhaps  10  tons  of 
melted  pig  iron  are  poured  into  a  hollow  pear-shaped  converter, 
Figs.  5,6  and  7,  lined  with  silicious  material.  Through  the  molten 


Fig.  5.     Section  Through  a  Mixer 

From  Stoughton's  "Metallurgy  of  Iron  and  Steel" 

Courtesy,  McGraw-Hill  Publishing  Company 

material  is  then  forced  25,000  .cubic  feet  of  cold  air  per  minute.  In 
about  four  minutes  the  silicon  and  manganese  are  all  oxidized  by 
the  oxygen  of  the  air  and  have  formed  a  slag.  The  carbon  then 
begins  to  oxidize  to  carbon  monoxide,  CO,  and  this  boils  up  through 
the  metal  and  pours  out  of  the  mouth  of  the  vessel  in  a  long  brilliant 
flame,  Fig.  8.  After  another  six  minutes,  the  flame  shortens  or 
'drops' ;  the  operator  now  knows  that  the  carbon  has  been  eliminated 
to  the  lowest  practicable  limit,  say  0.04  per  cent,  and  the  operation 
is  stopped.  So  great  has  been  the  heat  evolved  by  the  oxidation  of 
the  impurities  that  the  temperature  is  now  higher  than  it  was  at 
the  start,  and  we  have  a  white-hot 
liquid  mass  of  relatively  pure  metal. 
To  this  is  added  a  carefully  calculated 
amount  of  carbon  to  produce  the  de- 
sired degree  of  strength  or  hardness, 
or  both;  also  about  1.5  per  cent  of 
manganese  and  0.2  per  cent  of  silicon. 
The  manganese  is  added -to  remove 
from  the  bath  the  oxygen  with  which  Fig  6>  Part8  of  converter 

it  has  become  Charged  during  the  Ope-  Courtesy  McGraw-Hill  Publishing  Company 


\.  ,N 


14 


STEEL  CONSTRUCTION 


ration  and  which  would  render  the  steel  unfit  for  use.  The  silicon 
is  added  to  get  rid  of  the  gases  which  are  contained  in  the  bath. 
After  adding  these  materials,  or  "recarburizing"  as  it  is  called,  the 
metal  is  poured  into  ingots  which  are  allowed  to  solidify,  and  then 
rolled,  while  hot,  into  the  desired  sizes  and  forms.  The  character- 
istics of  the  Bessemer  process  are:  (a)  great  rapidity  of  purification, 
say  ten  minutes  per  "heat";  (b)  no  extraneous  fuel  is  used;  and 


Fig-  7.     Section  Through  Bessemer  Converter  While  Blowing 
From  Stoughton's  "Metallurgy  of  Iron  and  Steel" 
Courtesy  McGraw-Hill  Publishing  Company 

(c)  the  metal  is  not  melted  in  the  furnace  where  the  purification 
takes  place. 

" Acid  Open- Hearth  Process.  The  acid  open-hearth  furnace  is 
heated  by  burning  within  it  gas  and  air,  each  of  which  has  been 
highly  preheated  before  it  enters  the  combustion  chamber.  A  sec- 
tion of  the  furnace  is  shown  in  Fig.  9.  The  metal  lies  in  a  shallow 
pool  on  the  long  hearth,  composed  of  silicious  material,  and  is 


STEEL  CONSTRUCTION 


15 


heated  by  radiation  from  the  intense  flame  produced  as  described. 
The  impurities  are  oxidized  by  an  excess  of  oxygen  in  the  furnace 
gases  over  that  necessary  to  burn  the  gas.  This  action  is  so  slow, 
however,  that  the  3  to  4  per  cent  of  carbon  in  the  pig  iron  takes  a 


Fig.  8      A  Bessemer  Blow 

From  Stoughton's  "Metallurgy  of  Iron  and  Sieel" 
Courtety  McGra\c~H\U  Publishing  Company 

long  time  for  combustion.  The  operation  is  therefore  hastened  iu 
two  ways:  (a)  iron  ore  is  added  to  the  bath,  and  (b)  the  carbon  is 
diluted  by  adding  varying  amounts  of  cold  steel  scrap.  The  steel 


16 


STEEL  CONSTRUCTION 


scrap  is  added  to  the  furnace  charge  at  the  beginning  of  the  process, 
and  it  takes  from  6  to  10  hours  to  purify  a  charge,  after  which 
we  recarburize  and  cast  the  metal  into  ingots.  The  characteristics 
of  the  open-hearth  process  are:  (a)  long  time  occupied  in  purifica- 
tion; (b)  large  charges  treated  in  the  furnace  (modern  practice  is 
usually  30  to  70  tons  to  a  furnace) ;  (c)  at  least  part  of  the  charge 
melted  in  the  purification  furnace;  and  (d)  furnace  heated  with 
preheated  gas  and  air,  Fig.  10. 

"Basic  Open- Hearth  Process.    The  basic  open-hearth  operation 
is  similar  to  the  acid  open-hearth  process,  with  the  difference  that  we 


Fig.  9.     Section  of  Regenerative  Open-Hearth  Furnace 

From  Stoughton's  "Metallurgy  of  Iron  and  Steel" 
Courtesy  McGraw-Hill  Publishing  Company 

add  to  the  bath  a  sufficient  amount  of  lime  to  form  a  very  basic 
slag.  This  slag  will  dissolve  all  the  phosphorus  that  is  oxidized, 
which  an  acid  slag  will  not  do.  We  can  oxidize  the  phosphorus  in 
any  of  these  processes,  but  in  the  acid  Bessemer  and  the  acid  open- 
hearth  furnaces  the  highly  silicious  slag  rejects  the  phosphorus,  and 
it  is  immediately  deoxidized  again  and  returns  to  the  iron.  The 
characteristics  of  the  basic-  open-hearth  process  are  the  same  as 
those  of  the  acid  open-hearth  with  the  addition  of:  (e)  lime  added  to 


18  STEEL  CONSTRUCTION 

produce  a  basic  slag;  (f)  hearth  lined  with  basic,  instead  of  silicious, 
material,  in  order  that  it  may  not  be  eaten  away  by  this  slag;  and 
(g)  impure  iron  and  scrap  may  be  used,  because  phosphorus,  and, 
to  a  limited  extent,  sulphur  can  be  removed  in  the  operation. " 

Rolling  the  Ingots.    The  steel  in  the  ingot  is  in  its  final  condi- 
tion as  to  chemical  composition,  Figs.  11  and  12,  and  must  now  be 


Fig.  11.     Steel  Ingots  Incased  in  the  Molds  and  Resting  on  Car 

From  Stoughton's  Metallurgy  of  Iron  and  Stee 

Courlrxy  MrGm w-llill  Publish iinj  Company 

worked  into  the  shapes  required  for  structural  uses.     This  is  done 
by  passing  the  steel  between  rolls. 

Rolls  are  used  in  pairs,  called  a  "two-high  mill",  as  shown  in 
Fig.  13,  or  in  sets  of  three,  called  a  ''three-high  mill",  as  shown  in 
Fig.  14.  As  the  piece  goes  through  the  same  mill  se-seral  times,  the 
two-high  mill  must  be  reversed  for  each  pass  or  else  the  piece  must 
be  taken  over  or  around  the  mill  between  the  successive  passes. 
These  disadvantages  are  eliminated  by  the  use  of  the  three-high 


STEEL  CONSTRUCTION 


19 


mill,  in  which  the  rolls  rotate  continuously  and  work  is  done  on  the 
piece  as  it  passes  back  and  forth. 
Blooming.  Before  going  to 
the  rolls,  the  ingot  is  placed  in  a 
furnace,  called  the  ''soaking  pit", 
in  which  it  is  heated  to  a  high 
temperature.  In  passing  between 
the  rolls,  Fig.  13,  a  heavy  pres- 
sure is  exerted  on  the  metal, 
which  reduces  it  in  thickness,  in-. 
creases  it  in  width  to  some  ex- 
tent, and  extends  it  greatly  in, 
length.  If  the  material  is  des- 
tined to  be  made  into  plates,  it 
is  rolled  into  a  slab  in  the  first 
set  of  rolls;  if  it  is  for  structural 
shapes,  the  ingot  will  be  turned 
alternately  from  side  to  edge  in 
passing  through  the  rolls  so  that 
it  will  be  kept  approximately  square  in  section  until  it  is  reduced 
to  the  proper  size  for  beginning  to  form  the  shape.  At  this  stage 
it  is  called  a  "bloom"  and  the 
rolls  are  called  "blooming  rolls", 
Fig.  15. 


Fig.  12.     Stripping  the  Ingots 
Courtesy  McGraw-Hill  Publishing  Company 


Fig.  13.     Action  on  Steel  in  "Two-High"  Mill       Fig.  14.     Action  on  Steel  in  "Three-High"  Mill 
Courtesy  McGraw-Hill  Publishing  Company  Courtesy  McGraw-Hill  Publishing  Company 

Roughing  and  Finishing  Holls.    The  next  step  is  to  pass  the 
steel  through  the  roughing  rolls.    These  rolls  are  grooved  in  such 


.20 


STEEL  CONSTRUCTION 


Fig    15.     "Two-High"  Blooming  Rolls 
Courtesy  Ufa  man.  Slccth  Cum  pony 


a  way  that  the  successive  passes  gradually  develop  the  metal  toward 
the  required  shape.  Finally  it  goes  through  the  finishing  rolls 
which  bring  the  section  to  the  required  shape  and  size.  This  process 
is  clearly  illustrated  by  Figs.  *16,  17,  18,  19,  and  20. 


Fig.   16.     "Three-High"  I-Beam  Roughing  Rolls 
Courtesy  Seaman,  Sleeth  Company 


*Catalogue  of  Phoenix  Roll  Works,  by  permission. 


STEEL  CONSTRUCTION 


Fig.   17       'Three-High"  I-Beam  Finishing  Rolls 
Courlesy  Seaman,  Sleeth  Company 


"HO  I  iff  II 


Fig.  18.     "Three-High"  Equal  Angle  Roughing  Rolls 
Courtesy  Seaman,  Sleeth  Company 


22 


STEEL  CONSTRUCTION 


Fig.  19.     "Three-High"  Equal  Angle  Finishing  Rolls 
Courtesy  Seaman,  Sleeth  Company 

Plate  Rolls.  A  three-high  set  of  plate  rolls  is  shown  in  Fig. 
21.  There  is  nothing  to  control  the  width  of  the  plates,  therefore 
the  edges  -of  plates  rolled  in  this  mill  will  be  uneven  and  must  be 
sheared  to  the  correct  width  after  the  rolling  is  completed.  Such 
plates  are  known  as  ' 'sheared  plates." 

Vertical  rolls  can  be  placed  in  front  of  the  horizontal  rolls  to 


Fig.  20.     "Three-High"  Z-Bar  Rolls 
Courtesy  Seaman,  Sleeth  Com  pa  MM 


STEEL  CONSTRUCTION 


23 


control  the  width,  as  shown  in  the  left-hand  view,  Fig.  22.     Such  a 
mill  is  called  a  "Universal  Mill"  and  the  plates  produced  by  it  are 


Fig.  21.     "Three-High"  Chill  Plate  Rolls 
Courtesy  Seaman,  Sleeth  Company 

called  "Universal  Mill  plates,"  or  edged  plates.  Fig.  22  is  a  special 
form  known  as  the  Grey  mill  and  is  used  by  the  Bethlehem  Steel 
Company  for  making  I-beams  and  column  sections.  Fig.  23  is  a 
3-high  Universal  Mill  manufactured  by  the  United  Engineering  and 
Foundry  Company,  Pittsburgh. 


H 


P 


V 


P 


P 
P 


I  IK    L'2.     Vnivorsul  Mill  for  Rolling  Bethlehem  Beams 

STEEL  SECTIONS— ADAPTABILITY  AND  USE 

Classification  of  Sections.  Structural  steel  members  are  gener- 
ally designated  by  the  shapes  of  their  cross  sections.  Thus  a  member 
whose  cross  section  has  the  shape  of  a  capital  letter  I  is  called  an 
I-beam.  The  other  important  sections  are  channels,  angles,  zees, 


STEEL  CONSTRUCTION  25 

tees,  and  H-sections,  whose  shapes  are  indicated  by  the  names. 
Round  and  square  members  are  called  "rods"  and  "bars".  Flat 
members  six  inches  wide  and  less  are  usually  designated  as  "bars" 
or  "flats".  Flat  members  wider  than  six  inches  are  designated  as 
"plates".  Structural  sections  are  frequently  designated  as  "plates" 
and  "shapes".  In  general,  the  structural  shapes  are  standard. 

Standard  Sections.  The  shapes  in  common  use  conform  to  the 
standards  of  the  Association  of  American  Steel  Manufacturers. 
These  standard  shapes  as  made  by  the  various  manufacturers  are 
identical  in  dimensions  and  weights;  therefore,  in  designing  it  is 
only  necessary  to  specify  the  sections  and  not  the  name  of  the 
manufacturer. 

Special  Sections.  In  addition  to  the  standard  sections,  most 
manufacturers  make  some  special  sections.  Some  of  these  are  now 
so  common  that  they  are  as  available  as  standard  sections,  but 
generally  it  is  advisable  for  the  designer  to  give  the  name  of  the  manu- 
facturer in  specifying  them.  The  handbooks  indicate  which  sections 
are  standard  and  which  are  special.*  The  designer  should  generally 
use  only  standard  sections.  This  matter 
is  given  full  consideration  elsewhere  in 
this  text.  Use  the  handbook  for  con- 
stant reference  in  the  following  discussion 
of  the  sections. 

I -Beams.  Standard  Sections.  An 
I-beam,  Fig.  24,  is  designated  by  the 
depth  and  the  weight  per  lineal  foot,  thus: 

12"   I  31  J#  Fig.  24.     Details  of  Standard 

The  standard  depths  are  3,  4,  5,  6,  7,  8, 

9,  10,  12,  15,  18,  20,  and  24  inches,  respectively.  For  each  depth 
there  are  several  standard  weights.  Most  of  the  mills  also  make 
some  special  weights,  viz: 

12"  deep  weighing  40  to  55  # 
15"  deep  weighing  60  to  80  # 
15"  deep  weighing  80  to  100# 
20"  deep  weighing  80  to  100  # 

*The  1903  edition  of  the  "Carnegie  Handbook"  used  the  term  standard  in  relation  to  beams 
and  channels  to  apply  to  the  minimum  weight  of  each  size.  It  is  preferable  to  limit  the  use  of 
the  term  to  the  sections  adopted  by  the  Association  of  American  Steel  Manufacturers. 


26  STEEL  CONSTRUCTION 

Carnegie  Sections.  The  Carnegie  Steel  Company  rolls  some 
additional  sizes  of  special  beams  which  are  similar  to  the  standard 
beams,  as  follows: 

24"  deep  weighing  105  to  115# 
18"  deep  weighing    75  id  100  # 

It  also  rolls  special  sizes  of  certain  depths  which  are  lighter  than  the 
minimum  weight  standard  beams.    They  are  as  follows: 

*10"  I  22  #  18"  I  46  # 

12"  I  27|  #  21"  I  57J  # 

15"  I  36  ^  24"  I  69|  # 

27"  I  83  # 

A  distinctive  feature  of  these  beams  is  that  the  fillets  connecting 

flange  to  web  form  a  compound  curve  instead  of  a  simple  curve  as 

in  the  standard  beams. 

Bethlehem  Sections.    The  Bethlehem  Steel  Companyt  makes  a 

series  of  special  I-beams  ranging  in  depth  from  8  to  30  inches. 
The  minimum  weights  of  these  beams  are  about 
V*?^Uy  10  Per  cent  less  than  the  minimum  weights  of 
the  corresponding  standard  beams.  The  section 
is  so  designed  that  the  theoretical  strength  of 
the  minimum  section  is  about  the  same  as  that 
of  the  standard  section.  This  is  accomplished 
by  putting  less  metal  in  the  web  and  more  in 
the  flanges.  Fig.  25  gives  the  dimensions  of 
the  Bethlehem  15"  I  38  #.  Comparison  with 
the  corresponding  standard  beam  shows: 


15"I38#  15"I42# 

Web  thickness                                         .28"  .41* 

Flange  width                                        6.66*  5.50* 

Moment  of  inertia                            442 .60  441 . 80 

The  Bethlehem  Company  also  makes  a  series  of  girder  beams 
ranging  in  depth  from  8  to  30  inches.    These  beams  are  much 


*  Apply  to  the  nearest  office  of  the  Carnegie  Steel  Company  or  the  Illinois  Steel  Company, 
for  a  circular  giving  the  properties  of  these  beams,  or  see  "Pocket  Companion/'  Carnegie  Steei 
Company,  1913. 

t  Complete  data  are  fciven  in  the^Corapany's  handbook. 


STEEL  CONSTRUCTION 


27 


heavier  than  either  the  standard  beams  or  the  Bethlehem  special 
beams  and  the  flanges  are  also  much  wider.  Fig.  26  gives  the 
dimensions  of  the  Bethlehem  girder  15"X73#. 

Efficiency  of  Minimum  Sections.    Note  in  the  handbook  that 
the  weights  of  beams  of  a  given  depth  _  I05&.  _ 

are  grouped.  The  beams  in  a  group 
are  rolled  with  the  same  rolls,  the  min- 
imum section  being  produced  when  the 
rolls  are  set  close  together,  and  the 
heavier  sections  being  made  by  spread- 
ing the  rolls.  In  this  change  the  depth 
remains  constant,  while  the  web  is  thick- 
ened and  the  flanges  widened.  In  Fig. 
27,  the  shaded  portion  represents  the  Fig  26'  Brthw*»  Girder  15'X73# 
minimum  section,  and  the  unshaded  portion  represents  the  metal 
added  to  produce  the  heavier  section.  From  this  it  is  clear  that  most 
of  the  added  metal  is  in  the  web,  and  is  not  placed  to  such  good  advan- 
tage as  the  metal  in  the  minimum  section.  The  increased  strength 
is  not  nearly  so  great  as  the  increased  weight.  For  example, 
compare  15"  I  42  #  with  15"  I  60#  of  the  same  group.  The  increase 

1  R 


/|  BB2^HH 
8' 
SLOPE 

•C4T 

sff/HDiUS 

7^"7^T-~—  ^ 

in  weight  is  18  pounds,  or  —=43%.  The  increase  in  strength 
as  indicated  by  the  change  in  the  moment  of  iner- 
tia from  441.8  to  538.6  is  96.8,  or 


Fig.  27.  Showing 
Method  of  In- 
creasing Section 
of  I-Beama 


ence  is  70.4,  or 


Thus  it  appears  that  the  minimum  weight  of  each 
group  is  the  most  efficient.  As  a  consequence  the 
range  in  weight  from  a  given  set  of  rolls  is  limited  to 
about  20  pounds.  When  a  greater  range  is  required 
for  a  given  depth  of  beam,  more  than  one  set  of 
rolls  is  used.  Now  compare  the  standard  15"  I  60$ 
and  the  special  15"  I  60  #.  Their  respective  mo- 
ments of  inertia  are  538.6  and  609.0.  The  differ- 
70.4 


.  =  13%.    This  illustrates  the  -advantage  of 


538.6 

having  the  additional  set  of  rolls.  More  than  one  set  of  rolls 
is  provided  for  12-inch,  15-inch,  18-inch,  20-inch  and  24-inch 
beams. 


STEEL  CONSTRUCTION 

PROBLEM 

Make  full-size  drawings  on  tracing  paper  of  the  following  sections: 


Standard 

15"    I    42# 

Standard 

15*     I    55# 

Special 

15"    I    60# 

Special 

15"    I    80# 

Special 

15"    I  100# 

Carnegie 

15"    I    36# 

Bethlehem 

15"    I    38# 

Bethlehem 

15"  GB  73# 

L 


Superimpose  these  tracings  and  note  the  difference  in  thickness  of  web,  width  of 
flange,  and  shape  of  fillets. 

Characteristics  and  Uses.  An  inspection  of  an  I-beam  section 
shows  it  is  much  stiffer  in  one  direction  than  in  the  other.  The  section 
is  designed  to  resist  bending  in  one  direction  only,  i.  e.,  in  the  plane 
of  the  web  of  the  beam.  The  I-beam  is  used  almost  exclusively  for 
this  purpose,  though  to  a  limited  extent  it  is 
used  in  built-up  columns.  When  used  in  a 
column,  it  is  economical  only  when  com- 
bined with  other  sections  to  give  stiffness  in 
both  directions.  It  is  sometimes  used  alone 
as  a  column  when  the  limitations  of  space 
offset  the  lack  of  economy  in  weight. 

Beams  less  than  6  inches  deep  are  not 
Fig.  28.   Details  of  Channel   of  ten  used  in  the  framework  for  buildings. 

On  many  jobs  the  minimum  is  8  inches. 

Channels.  Standard  and  Special  Sections.  A  channel,  Fig.  28, 
is  designated  by  the  depth  and  the  weight  per  lineal  foot,  thus: 

15"  C33# 

The  standard  depths  are  3,  4,  5,  6,  7,  8,  9,  10,  12,  and  15  inches, 
respectively.  For  each  depth  there  are  several  weights.  A  number 
'  of  special  sizes  and  weights  are  made  but  they  are  not  much  used 
for  structural  purposes.  The  Cambria  Steel  Company  makes  a 
group  of  channels  18  inches  deep,  weighing  from  45  to  60  pounds. 

The  weights  of  channels  are  increased  in  the  same  manner  as 
the  weights  of  beams,  Fig.  29,  and  the  comments  regarding  beams 
in  this  respect  apply  to  them. 

Characteristics  and  Uses.  Channels,  like  beams,  are  much 
stronger  in  one  direction  than  in  the  other.  This  makes  them  suit- 


STEEL  CONSTRUCTION 


29 


Fig.  29.  Show- 
ing Method  of 
Increasing  Sec- 
tion of  Chan- 


able  for  use  as  beams  when  the  loads  are  applied  in  the  plane  of  the 
web.  However,  they  are  not  so  economical  as  I-beams  and  require 
more  lateral  support  to  keep  them  from  buckling. 
Hence,  they  are  not  used  for  this '  purpose  except 
when  there  is  some  condition  which  makes  them 
specially  suitable.  This  occurs  around  wellholes  in 
floors,  against  walls,  where  nailing  strips  are  to  be 
bolted  on,  in  wall  spandrels  or  lintels,  etc. 

The  most  important  use  of  channels  is  in  the 
construction  of  columns  and  truss  members.  For 
this  purpose  they  are  used  in  pairs  connected  to- 
gether with  lacing,  tie  plates,  or  cover  plates.  They 
are  also  used  to  some  extent  for  girder  flanges  and 
for  many  miscellaneous  purposes.  , 

Angles.    Standard  and  Special  Sections.    There 
are  two  styles  of  angles:  angles  with  equal  legs  and  angles  with 
unequal  legs,  Fig.  30.    An  angle  is  designated  by  the  lengths  of  the 
legs  and  the  thickness  or  the  weight  per  lineal  foot,  thus: 

L  4"  X  4"  X  I" 
or  L4"X4"X  15.7  #. 

L  6"  X  3i"  X  f 
or  L6"X3f  Xll.7# 

The  standard  sizes  of  angles  with  equal  legs  are  1J,  2,  2J,  3,  3J, 
4,  6,  and  8  inches,  respectively.  There  are  a  number  of  special  sizes, 
the  most  important  of  which  is  5  inches.  The  If -inch  angle  is 
seldom  used  in  structural  work. 

The  standard  sizes  of 
angles  with  unequal  legs 
are  1\"  X  2",  3"  X  2J*,  3J" 
X2i",  3|"X3",  4"X3", 
5*X3',  5'X3i",  6"X3i", 
6"  X  4".  The  important 
special  sizes  usually  obtain- 
able are  3'  X  2",  1"  X  3i",  8"  X  6". 

Each  size  of  angle  is  furnished  in  several  thicknesses  varying 
by  tV  inch.  Although  some  of  the  smaller  sizes  of  angles  are  made 


-THICKNESS  SHORT  L£G      f 

Fig.  30.     Details  of  Angle  Sections 


30  STEEL  CONSTRUCTION 

in  less  thickness  than  J  inch,  this  is  the  minimum  that  should  be 
used  for  structural  purposes.    On  important  work  the  minimum 
should  be  f  inch.    The  minimum  and  maximum  thickness,  for  the 
several  sizes  are  given  in  the  handbook  and  need  not  be  repeated  here. 
Angles  are  increased  from  the  minimum  thickness  by  spreading 
the  rolls.     In  Fig.  31  the  minimum  thickness  is  shaded  and  the 
added  metal  unshaded.     As  the  thickness  is  increased,  a  correspond- 
ing amount  is  added  to  the  length  of  each  leg.     In 
the  case  of  larger  sizes,  some  mills  use  two  sets  of 
rolls,  as  has  been   described  for    I-beams.    This 
additional  length   of   the  legs  of   angles  must  be 
taken  into  account  in  allowing  for  clearance.    The 
Fig.   31.     showing  actual  length  of  legs  for  any  angle  is  easily  com- 
Sc^n'oTA^-  puted,  thus:     L  3"  X  3"  X  f ;  minimum  thickness 
for  this  size  J",  increase  over  minimum  f",  length 
of  leg  3"  +  f  =  3|". 

PROBLEM 

Compute  the  actual  lengths  of  legs  for  the  maximum  thickness  of  all  the 
standard  and  special  angles  listed  in  the  handbook.  Assume  a  second  set  of  rolls 
is  used  on  the  following  sizes:  S'X^XiV';  4"X4"Xi";  Sfc'XSi'X**; 

5"xsrxr;  5"x3"xr;  4"xsrxr;  4"x3"xr;  6"x3rxiV; 
6*X4"XiV';  5"X5"XjV';  6"X6"XH";  7"X3rxf;  S"XQ"X%": 
8"X8"Xi". 

Record  the  results  in  the  handbook  in  the  tables  of  "Properties." 

The  results  in  the  above  problem  may  not  agree  with  the  sizes 
of  angles  furnished  by  the  various  mills  but  will  be  sufficiently  exact 
for  the  uses  of  the  designer. 

Characteristics  and  Uses.    Angles  are  the  most  adaptable  of  the 
structural   sections.    They   are   used  with 
plates  or  other    shapes   in   built-up  mem- 
bers, such  as  columns,  plate  girders,  etc.; 
for  connecting  members  together,  as  beams 
and   girders    to   columns;    as   beams    for 
special    conditions   of  loading,   as   lintels;      Fig- 32-   Details  of  Zee  Bar 
singly  or  in  pairs  as  struts;  singly  or  in  pairs  as  tension  members. 

Zees.  Standard  Sections.  A  Zee,  Fig.  32,  is  designated  by  its 
nominal  depth  and  thickness,  thus: 

Z3"X|" 
The  sizes  listed  by  the  Carnegie  Steel  Company  are  3,  4,  5,  and  6 


STEEL  CONSTRUCTION  31 

inches,  respectively.  The  thicknesses  vary  by  TV  inch.  The  mini- 
mum and  maximum  thicknesses  are: 

for  3"  Z,  r  and  ft' 
for  4'  Z,  fand  f 
for  5"  Z,  A"  and  «* 
for  6"  Z,  f *  and  }' 

Zees  are  increased  in  thickness  by  spreading  the  rolls.  In  Fig.  33 
the  shaded  portion  indicates  the  minimum  section,  and  the  unshaded 
part  the  additional  section.  The  thickness  of  its 
web  and  flanges  are  increased  equally,  and  thereby 
the  depth  of  web  and  width  of  flange  are  increased 
by  the  same  amount.  Three  sets  of  rolls  are  used  . 

Fig.  33      Showing 

for  each  depth,  so  that  the  overrun  is  yV  inch  for  "JJjSng  Section 
3-inch  zees  and  J  inch  for  larger  sizes.  of  Zee3 

Uses.  Zee  bars  have  been  used  extensively  for  columns,  but 
they  are  rapidly  becoming  obsolete  and  should  not  be  used  unless 
there  is  some  special  reason  for  so  doing. 

Tees.  Standard  Sections.  A  Tee,  Fig.  34,  is  designated  by  the 
width  of  flange,  length  of  stem,  and  weight  per  lineal  foot,  thus: 

T4"  X  3"X9.3#  T3"  X  4"X9.3# 

always  giving  the  width  of  flange  first. 

Some  recent  handbooks  do  not  list  tees.  The  sizes  that  have 
been  available  range  from  T  X  1"  X  1.0#  to  5"  X  3"  X  13.6#  with 
more  than* 50  intermediates.  These  are  listed  and  their  properties 
given  in  the  Carnegie  Steel  Company's  "Pocket  Companion",  1913. 
edition. 

Characteristics  and  Uses.  As  indicated  above  tees  are  going 
out  of  use,  and  as  the  demand  decreases  they  will  become  more 


Fig.  34.     Typical  Tee  Sections 


difficult  to  obtain.  The  section  is  not  an  economical  one  for  the 
common  uses  of  structural  steel.  It  is  not  efficient  as  a  beam  or 
as  a  strut,  and  is  not  suited  for  use  in  built-up  sections. 


32 


STEEL  CONSTRUCTION 


It  is  well  adapted  for  supporting  book  tile  in  ceiling  and  roof 
construction,  Fig.  35.    In  cases  where  the  T-section  is  needed  to 


Fig.  35.     Section  Showing  Tees  Supporting  Book  Tile 

meet  any  special  condition  it  can  be  made  up  of  two  angles  placed 
back  to  back.  In  this  manner  a  large  variety  of  tees  can  be  made. 

Plates.  Standard  Sizes.  A  Plate,  Fig.  36,  is  designated  by 
its  width  and  thickness,  thus: 

PL  48"  X  TV 
or  by  its  width  and  weight  per  square  foot,  thus:' 

PL  36"  X  10.2  # 

The  former  method  is  used  on  design  drawings  for  structural  steel 
work,  and  the  latter  on  mill  orders  and  shop  details,  also  on  design 
drawings  for  tank  work. 

Plates  are  made  in  thicknesses  varying  by  iV  inch  from  y\  inch 
up  to  2  inches.  Steel  plates  thinner  than  i\  inch  are  called  "sheets'* 
and  are  not  used  for  structural  work.  The  minimum  thickness  com- 
monly used  is  \  inch,  and  on  many  jobs  nothing  less  than  f  inch  is  per- 
mitted. Plates  thicker  than  1  inch  are  seldom  used  on  account  of 


-  THICKNESS 


Fig.  36.     Rolled  Steel  Plate 


difficulty  in  punching.    When  a  greater  thickness  is  needed,  it  is 
made  up  of  two  or  more  plates. 

Styles.    There  are  two  styles  of  plates:    the  Universal  Mill 
Plate,  or  Edged  Plate,  and  the  Sheared  Plate. 


STEEL  CONSTRUCTION 


33 


The  Universal  Mill  Plate  is  rolled  to  exact  width,  the  width 
being  controlled  by  a  pair  of  vertical  rolls  as  previously  described 
and  illustrated,  Fig.  22.  They  vary  in  width  by  intervals  of  1  inch 
from  6  inches  to  48  inches. 

Sheared  plates,  as  the  name  indicates,  are  sheared  to  required 
width  after  rolling.  The  stock  sizes  range  in  width  from  24  inches 
to  132  inches  in  intervals  of  6  inches,  but  they  can  be  furnished  in 
any  intermediate  width,  even  in  fractions  of  an  inch. 

The  extreme  lengths  of  plates  that  can  be  furnished  are  given 
in  the  handbooks.  This  data  should  be  consulted  to  determine 


r — ** — i 

i_     J^ 


RADIUS  0.31' 


(Cf.745- 


CARNEGIE  -H-SXJ4 O  BETHLEHEM- H- 14X98.6 

Fig.  37.     Typical  H-Sections 

whether  the  required  lengths  can  be  obtained.  In  many  cases  the 
web  plates  of  girders  must  be  spliced  on  this  account. 

Plates  alone  are  not  used  for  structural  members.  They  are 
used  in  built-up  members,  such  as  columns  and  girders;  for  web  and 
cover  plates;  and  to  connect  members  together. 

H-Sections.    The  H-section,  Fig.  37,  is  designated  by  the  name 
of  the  maker,  the  depth,  and  the  weight  per  lineal  foot,  thus: 
Carnegie       8"  H  34.0  # 
Bethlehem  14"  H  98.8  # 

The  H-section  is  not  standard.  At  this  time  it  is  made  only  by  the 
Carnegie  Steel  Company  and  the  Bethlehem  Steel  Company.  The 
Carnegie  H's*  are 

8"H34.0#  5"H  18.7  # 

6"  H  23.8#  4"  H  13.6# 

There  is  but  one  weight  for  each  size. 

*Apply  to  the  nearest  office  of  the  Carnegie  Steel  Company,  or  the  Illinois  Steel  Company, 
lor  circular  giving  properties,  or  see  Carnegie  Steel  Company's  Pocket  Companion,  1913  edition. 


34 


STEEL  CONSTRUCTION 


The  nominal  sizes  of  the  Bethlehem  H-sections  are  8,  9,  10,  11, 
12,  13,  and  14  inches,  respectively.  The  actual  sizes  range  from 
7J  inches  to  16J  inches  in  intervals  of  J  inch.  The  extreme  weights 
are  34.6  pounds  and  291.2  pounds  per  lineal  foot. 

The  H-sections  are  designed  for  use  as  columns  and  struts. 
They  are  not  intended  to  be  used  in  built-up  members,  except  a 
special  section  which  is  designed  to  be  increased  by  adding  flange 
plates. 


Fig.  38.     Miscellaneous  Special  Sections 


Miscellaneous  Sections.  In  addition  to  the  regular  structural 
sections  just  described  there  are  a  number  of  special  sections,  Fig. 
38,  with  which  the  designer  should  be  familiar,  viz: 

(a)  Railroad  Rails  (e)  Steel  Sheet  Piling 

(b)  Wide-Flanged  Channels  (f)  Steel  Railroad  Ties 

(c)  Bulb  Beams  (g)  Square  Root  Angles 

(d)  Bulb  Angles  (h)  Hand  Rail  Tees 

(i)  Checkered  Floor  Plates 

These  sections  are  not  often  used  in  steel  construction  for  buildings, 
but  occasionally  conditions  have  to  be  met  to  which  some  of  them 
are  specially  suited. 


STEEL  CONSTRUCTION 
PROPERTIES  OF  SECTIONS 


35 


Under  the  heading  "Properties  of  Sections"  the  handbooks  give 
tables  of  the  numerical  values  of  the  various  functions  of  the  sec- 
tions. Referring  to  these  tables,  certain  items  need  no  explanation, 
viz:  dimensions;  thickness  of  metal;  area;  weight  per  lineal  foot. 
Other  items  are  not  self-evident  and  will  be  explained  in  detail. 

Center  of  Gravity  (C.G.).  See  "Strength  of  Materials"  for 
definition.  The  I-beam,  H-section,  and  Z,  Fig.  39,  being  symmetrical 


e 


3= 


V 


Fig.  39.     Location  of  Center  of  Gravity  of  Sections.     Values  of  x,  x'.  and  x'  to  be  taken  from 
Tables  in  Handbook 

about  both  axes,  the  center  of  gravity  is  in  the  center  of  the  web 
and  no  values  are  given  in  the  handbook  tables.  The  C-section, 
Fig.  39,  is  symmetrical  only  about  the  axis  which  is  perpendicular 
to  the  web;  the  center  of  gravity  must,  therefore,  lie  on  this  axis. 
The  table  gives  the  distance  of  the  center  of  gravity  from  the  back 
of  the  channel. 

Angles  not  being  symmetrical  about  either  axis,  the  center  of 
gravity  must  be  located  by  dimensions  from  the  backs  of  both  legs. 
If  the  legs  are  equal,  both  dimensions  are  the  same;  if  the  legs  are 
unequal,  the  dimensions  are  unequal,  the  distance  from  the  short 
leg  x'  being  greater  than  that  from  the  long  leg  x,  Fig.  39. 


36  STEEL  CONSTRUCTION 

The  position  of  the  center  of  gravity  must  be  known  in  order 
to  compute  the  moment  of  inertia  of  the  section  and  the  moments 
of  inertia  of  built-up  members.  The  former  values  are  given  in 
the  tables;  the  latter  must  usually  be  computed  by  the  designer. 

Illustrative  Example.  Compute  the  position  of  the  center  of 
gravity  of  L4"  X  4"  X  ¥>  disregarding  fillets  and  rounded  corners, 
Fig.  40.  Divide  the  angle  into  two  rectangles  (1)  and  (2)  as  shown. 
Their  centers  of  gravity  are  at  ct  and  c2. 

Area  of  (1)      4  ;/  X  V  •*  2.00  sq.  in. 

Area  of  (2)      3 J"  X  |"  =  1.75  sq.  in. 

Total  area  3.75  sq.  in. 

Moments  about  a'  a'  for  (1)  =  2.00  X    \  =  0.50 

Moments  about  a'  a'  for  (2)  =1,75  X  2J  =  3.94 

Total  moment  4.44 

TV  *  4-44 

Distance  x  =  — -  =  1.18 

Similar  computations  apply  about 
the  axis  b'b'  and  give  the  same  result. 


Compute  the  position  of  the  center  of 
gravity  of  the  following: 


15"C33# 

Moment  of  Inertia  (7).    Refer 
to  "Strength  of  Materials"  for  defi- 
j^  nition   and   method  of  computing 

Fig.  4oa' Diagram  showing  computation     moment  of   inertia.     Moment  of 
of  Position  o^cen^r  of  Gravity  inertia  js  designated  by  the  letter 

7.      When  a  subscript    is    added 

it  indicates  which  axis  is  used.  Thus  70  means  the  moment  of 
inertia  about  the  axis  a.  Note  that  this  symbol  is  the  same  as  is 
used  for  the  beam.  Care  must  be  taken  to  avoid  confusion.  The 
meaning  can  be  determined  in  each  case  by  the  context.  The 
tables  in  the  handbook  give  the  value  of  7  about  both  of  the  rec- 
tangular axes  of  the  section  and,  in  the  case  of  angles,  about  a 
diagonal  axis  also.  The  position  of  this  diagonal  axis  is  so  chosen 


STEEL  CONSTRUCTION 


37 


as  to  give  the  minimum  value  of  7.    For  I-beams  and  channels  the 
minimum  value  is  about  the  axis  parallel  to  the  web. 

The  moment  of  inertia  enters  into  the  formulas  for  bending 
and  for  deflection.  It  is  also  used  in  computing  the  radius  of  gyra- 
tion of  columns.  Its  values  are  given  in  the  handbooks  for  the 
structural  shapes  and  for  plates,  but  it  must 
be  computed  for  most  built-up  sections,  espe- 
cially for  plate  girders.  The  factors  entering 
into  the  computation  of  the  moments  of  inertia 
are  always  in  inches. 

Illustrative  Examples.     1.     Compute  Ia 
and  /6  for  the  plate  shown  in  Fig.  41. 

1 


/a=:_X8Xl  X 


X  1  X  8X8X8  =  42§ 


Fig.  41.     Diagram  for  Moment 

of  Inertia  of  Rectangular 

Plate 


2.    Compute  Ia  for  the  plate  girder 
section  in  Fig.  42  made  of  1  PI.  42"  X  1*  and  i- 
4Ls  6"  X  6"  X  y. 

for  1  PI.  42"  X  y         Ia  (from  tables)  =3087 
for  4  Ls  6"  X  6"  X  i"   lc  (from  tables) 

4  X  19.91        =     80 
for4  Ls6*X6*  X  \'f  /04  X  5.75  X 

19.57  X  19.57  =  8809 


Deductions  for  rivet  holes  at  m 
Area  of  2  holes  =  2  X  1J*  X  F  = 

2.625  sq.  in. 

For  1  hole  Id  =  T'i  X  11*  X  V  X  V 
X  |"  =  -08 

(a  value  so  small  that  it  is 

neglected) 
/0=  2.625  X  18.75  X  18.75  = 


11.976 


11   rvRO   Fig.  42.     Diagram  for  Moment 
11  ,053        of  Inertia  of  Plate  Girder 


38 


STEEL  CONSTRUCTION 


PROBLEMS 

1.  Compute  the  values  of  /  for  the  section  in  Fig.  43.  Deduct  rivet 
holes.  The  section  is  made  up  of  4  Ls  G"X4"X  iV  connected  with  lacing  bars 
(lacing  not  figured). 

2.     Compute  the  values  of  /  for  the 
section  shown  in  Fig.  44. 

1  C  12'7X20J# 
1  L    4"X3"X|" 

The  axes  a  a  and  b  b  are  through  the 
center  of  gravity  The  section  not  being 
symmetrical,  the  position  of  the  center  of 
gravity  must  be  computed. 

Radius   of  Gyration  (r).    The 

radius  of  gyration  is  a  value  de- 
rived from  the  moment  of  inertia,  but  as  its  definition  involves  higher 
mathematical  relations  it  need  not  be  given  here.  It  is  reoresented 
by  r,  and  is  expressed  in  inches. 

The  radius  of  gyration  is  derived  from  the  moment  of  inertia 
by  dividing  by  the  area  A  in  square  inches  and  taking  the  square 
root  of  the  result.  This  is  expressed  by  the  formulas 

7 


Fig,  43.     Diagram  for  Moment  of  Inertia 
of  Four  Angles 


Illustrative  Examples.  1.  Referring  to  Fig. 
41,  the  value  of  Ib  =  42f ;  and  A  =  8X1=8 
sq  in.  Therefore  r2  =  42§-fS  =  5j,  or  r=^5J 
=  2.31". 

.2.    Referring  to  Fig.  42,  the  value  of  7a  = 
Fig.  44.     Diagram  for  1 1,976  (disregarding  rivet  holes).    To  find   the 

Moment   of   Inertia   of          j*  £  j.' 

Channel  and  Angle  TadlUS  OT  gyration 

/I  PL  42"  X  |"        =-21  sq.  : 


44 


*Refer  to  the  textbook  on  Arithmetic  for  method  of  extracting  the  square  root.     Tables 
are  given  in  the  handbooks  from  which  the  values  can  be  taken. 


STEEL  CONSTRUCTION  39 

PROBLEMS 

1.  Compute  the  values  of  r  for  the  sections  given  in  Figs.  43  and  44. 

2.  Check  the  values  given  in  the  handbook  for  r  fora  12*  I  31  f#. 

The  radius  of  gyration  is  used  in  the  column  formula  as  explained 
later  in  the  text. 

,  Section  Modulus    I  —  1.    In  the  formula  for  the  resisting  mo- 

ment of  sections  subjected  to  bending  occurs  the  expression  -,  in 

c 

which  I  is  the  moment  of  inertia  and  c  is  the  distance  from  the 

neutral  axis  to  the  extreme  fiber  of  the  section.    -  has  a  definite 

c 

value  for  each  section,  and  is  called  the  section  modulus.  It  saves 
one  operation  in  arithmetic  to  have  these  values  given  for  the  various 
sections  and  they  are  given  in  the  handbooks.  As  indicated  by  the 

fraction  -,  the  value  of  the  section  modulus  is  determined  by  divid- 
c 

ing  the  moment  of  inertia  by  the  value  of  c. 

Illustrative  Examples.     1.    Compute  -for  an  8"  I  18  #  about 

the  axis  perpendicular  to  the  web. 

From  the  table,  7  =  56.9.    The  distance  c  is  half  the  depth  =  4" 


c"    4 
2.    Compute  -  for  a  channel  1  2"X  20.  5  #  about  the  axis  par- 

allel to  the  web.     Not  being  a  symmetrical  section  it  has  two  values; 
From  handbook,  7  =  3.91;  c=   (2.94  -.70)   =2.24,  and  c  =  0.70. 
7     3.91      -  -,       ,7    3.91 


PROBLEM 

Compute  the  values  of  -  for 

15"  I  42#  about  axis  parallel  to  web 

9'  I  21#  about  axis  perpendicular  to  web 

15*  I  33#  about  axis  perpendicular  to  web 

L  S'XS'Xt*  about  axis  at  45°  to  legs 

L  6*X4ir  X  3*  about  axis  parallel  to  short  leg 

Miscellaneous  Properties.  The  handbooks  include  in  the 
tables  values  of  other  properties  of  sections  such  as  Coefficient  of 
Strength,  Coefficient  of  Deflection,  and  Resisting  Moment. 


40  STEEL  CONSTRUCTION 

Strictly  speaking,  these  are  not  properties  of  the  sections,  as  they 
depend  upon  the  value  of  the  unit  stress.  They  will  be  discussed 
in  the  text  relating  to  beams. 

GENERAL  INFORMATION 

Price  Basis.  The  designer  needs  to  be  posted  on  the  basis  of 
prices  for  structural  steel.  For  a  number  of  years  Pittsburgh, 
which  has  been  the  recognized  center  of  steel  production,  has  been 
the  basing  point  for  steel  prices.  Given  a  certain  price  for  steel  at 
Pittsburgh,  the  price  at  any  other  point  is  determined  by  adding 
to  the  base  price  the  freight  from  Pittsburgh.  Thus,  if  the  price 
of  steel  at  Pittsburgh  is  SL50  per  hundred  pounds,  the  price  in  Chi- 
cago is  SI. 68  per  hundred  pounds,  the  freight  rate  being  (at  the  time 
of  writing)  18  cents  per  hundred  pounds. 

Certain  sizes  of  material  are  called  "base"  sizes.  They  are 
usually  sold  at  a  uniform  price.  The  base  sizes  are:  I-beams,  3 
inches  to  15  inches,  inclusive;  angles,  3  inches  to  6  inches  inclusive; 
channels,  3  inches  to  15  inches  inclusive;  tees,  3  inches  and  over; 
zees,  all  sizes.  I-beams  over  15  inches,  angles  over  6  inches,  and 
angles  and  tees  under  3  inches  are  charged  for  at  a  higher  rate, 
usually  10  cents  per  hundred  pounds,-  above  base  price.  Special 
-ections  and  sections  rolled  exclusively  by  one  manufacturer  are 
sold  at  prices  varying  from  the  base  price  according  to  market 
conditions.  The  base  price  itself  varies  from  time  to  time,  usually 
from  SI. 25  per  hundred  pounds  to  SI. 50  per  hundred  pounds;  occa- 
sionally it  goes  beyond  these  limits. 

Mill  and  Stock  Orders.  Structural  steel  orders  are  handled 
on  two  bases:  (a)  based  on  securing  the  plain  material  for  the  job 
from  the  rolling  mills;  (b)  based  on  securing  it  from  stock.  Of 
course  there  may  be  a  combination  of  the  two. 

The  mill  basis  is  cheaper,  as  it  eliminates  waste,  saves  expense 
of  handling,  saves  interest  cost  on  the  value  of  material,  and  may 
save  a  profit  or  premium  demanded  by  the  dealer  for  quick  service. 
Consequently  all  work  is  carried  out  on  the  mill  basis,  if  the  time 
allowed  for  completion  permits  it  to  be  done. 

When  the  material  is  to  be  furnished  on  the  mill  basis,  the 
engineer  who  makes  the  detail  drawings  or  the  engineering  depart- 
ment of  the  fabricating  company  makes  a  list  of  the  individual 


STEEL  CONSTRUCTION  41 

pieces  required.  These  pieces  are  then  ordered  from  the  rolling 
mills,  cut  to  the  lengths  required  (a  small  variation  in  length  is 
usually  allowed;  short  pieces  are  usually  ordered  in  multiple  lengths). 
Thus  there  is  practically  no  waste  of  material. 

Material  carried  in  stock  is  ordered  from  the  rolling  mills  in 
lengths  as  long  as  can  be  handled  conveniently.  The  lighter  sec- 
tions are  ordered  in  lengths  of  30  feet  and  36  feet,  and  the  heavier 
sections  in  lengths  of  60  feet.  In  cutting  this  stock  material  there 
is  necessarily  considerable  waste.  This  stock  material  is  not  usually 
available  direct  from  the  rolling  mills.  The  dealers  in  stock  are 
usually  fabricating  companies,"  jobbers,  or  brokers.  They  charge 
an  advance  in  price  over  the  mill  price  to  cover  waste,  handling, 
cutting,  and  other  expenses  incidental  to  the  business,  and  to  cover 
such  profit  as  the  market  condition  may  permit.  This  advance 
in  price  varies  from  10  cents  to  50  cents  per  hundred  pounds. 

Stocks  of  plain  material  are  carried  in  all  the  larger  cities. 
Printed  lists  of  the  material  on  hand  are  issued  at  frequent  intervals. 
These  lists  should  be  consulted  and  used  as  a  guide -in  selecting  the 
sections  that  are  to  be  used  in  all  cases  where  stock  is  required. 

Whether  mill  or  stock  material  will  be  used  depends  upon  the 
size  of  the  job  and  the  time  service  required.  Small  jobs,  say  less 
than  100  tons,  will  usually  be  taken  from  stock  unless  only  one.  or 
two  sections  are  required.  If  delivery  of  fabricated  material  is 
required  within  60  days,  it  will  usually  have  to  be  taken  from  stock. 
Even  for  much  more  extended  deliveries,  all  or  part  of  the  material 
must  be  taken  from  stock,*  if  there  is  a  great  demand. 

Variation  in  Weight.  Attention  is  called  to  the  provision  in 
the  specifications,  p.  360,  which  permits  a  slight  variation  in  the 
weight  of  the  finished  steel  as  compared  with  its  theoretical  weight. 
This  variation  in  the  case  of  sections  other  than  plates  is  2.5  per  cent 
above  or  below  the  theoretical  weight.  This  represents  the  prac- 
ticable limits  in  adjusting  the  rolls  of  the  mill.  The  variation 
applies  to  individual  pieces  and  not  to  a  bill  of  steel  as  a 
whole;  some  pieces  will  be  overweight  and  some  underweight, 
so  that  the  average  on  a  bill  of  considerable  size  should  agree 
very  closely  with  the  theoretical  weight.  In  the  case  of  plates, 

*Apply  to  the  nearest  dealer  for  a  copy  of  his  stock  list.  Use  it  in  solving  the  problems  in 
this  book. 


42  STEEL  CONSTRUCTION 

a  much  larger  variation  is  allowed,  amounting  in  some  cases  to  as 
much  as  18  per  cent.  It  will  be  noticed  that  this  variation  is  greater 
when  plates  are  ordered  to  be  of  a  certain  gage  or  thickness  than 
it  is  when  they  are  ordered  to  be  of  a  certain  weight.  The  reason 
for  this  is  that  plates  are  slightly  thicker  in  the  middle  than  they 
are  along  the  edges  and,  therefore,  as  the  thickness  must  necessarily 
be  measured  near  the  edge,  there  is  an  excess  of  metal  near  the 
middle  of  the  plate  wrhich  is  not  counted.  This  excess  is  due  to  the 
springing  of  the  rolls.  Plates  can  be  ordered  by  weight,  that  is, 
to  have  a  certain  weight  per  square  foot  of  surface,  and  when  so 
ordered  the  allowable  variation  is  less  because  the  rolls  can  be 
adjusted  to  give  the  average  weight.  The  result  is  that  the  fabri- 
cating shop  usually  orders  large  plates  by  wreight  per  square  foot. 
In  a  job  involving  a  large  amount  of  plate  \vork,  as  for  chimneys, 
tanks,  etc.,  this  may  become  a  matter  of  importance,  but  for  build- 
ing work  a  relatively  small  number  of  plates  are  required  and  it  is 
not  customary  to  specify  them  by  weight,  but  by  thickness. 

QUALITY  OF  MATERIAL 

Reliability  of  Structural  Steel.  Structural  steel  is  the  most 
reliable  material  used  in  building  construction.  Its  manufacture 
has  been  a  continuous  development  to  the  extent  that  the  quality 
of  material  produced  is  under  almost  absolute  control.  The  ingredi- 
ents are  tested  and  measured  before  being  put  into  the  furnace,  and 
the  product  is  analyzed  and  tested  physically  to  make  sure  that  it 
fulfills  the  required  standards;  so  that,  with  a  reasonable  amount  of 
inspection  and  test,  the  purchaser  can  have  definite  assurance  that 
he  is  securing  the  quality  of  material  which  he  needs. 

The  manufacturers  and  users  of  structural  steel  have  co-oper- 
ated in  developing  the  material  in  order  to  attain  the  most  prac- 
ticable results.  On  the  one  hand,  the  manufacturers  have  insisted 
on  keeping  the  quality  such  as  to  make  its  manufacture  commercially 
satisfactory.  On  the  other  hand,  the  users  of  steel  have  demanded 
the  best  material  that  it  is  possible  to  make  and  still  keep  within 
reasonable  limitation  of  cost  of  manufacture. 

STANDARD  SPECIFICATIONS 

As  a  result  of  the  efforts  of  the  manufacturers  and  users, 
Standard  Specifications  ha.ve  been  formulated  covering  the  quality 


STEEL  CONSTRUCTION  43 

of  structural  steel.    There  are  three  sets  of  specifications  that  may 
safely  be  used,  viz:* 

(a)  Manufacturers'  Standard  Specifications  for  Structural 
Steel— Class  Bt 

(b)  Standard  Specifications  for  Structural  Steel  for  Build- 
ings,  adopted   by  the  American  Society  for  Testing 
Materials  (Given  in  full  p.  359) 

(c)  Specifications   for   Structural    Steel,    adopted   by   the 
American  Railway  Engineering  Association 

Comparison  of  Specifications.  A  brief  comparison  of  the  pro- 
visions of  these  three  sets  of  specifications  is  of  interest. 

Range  of  Application.  The  specifications  (a)  and  (b)  are 
intended  primarily  to  apply  to  steel  for  building  work,  whereas  (c) 
is  for  railway  bridges.  In  buildings,  the  greater  part  of  the  load  to 
be  supported  is  permanent  or  dead  load.  The  variable  or  live  load 
usually  is  applied  gradually,  without  shock  or  vibration.  In  railway 
bridges  the  conditions  are  quite  different.  The  permanent  load  for 
a  short  span  is  the  smaller  part  of  its  capacity.  The  live  load,  being 
much  larger  than  the  dead  load  and  being  applied  quickly,  produces 
great  shocks  and  vibration.  Because  of  these  conditions,  specifica- 
tion (c)  is  more  rigorous  in  its  requirements  than  are  (a)  and  (b). 

Process  of  Manufacture.  Specification  (c)  requires  the  open- 
hearth  process  of  manufacture;  (a)  and  (b)  permit  either  open- 
hearth  or  Bessemer. 

Chemical  Analysis.  Specification  (c)  requires  the  chemical 
analysis  to  report  the  percentages  of  sulphur,  phosphorus,  carbon, 
and  manganese,  and  limits  the  amount  of  sulphur;  (a)  and  (b)  limit 
the  phosphorus. 

Tensile  Strength.  Specification  (c)  places  the  desired  ultimate 
tensile  strength  of  steel  sections  at  60,000  pounds  per  square  inch, 
allowing  a  variation  of  4000  pounds,  thus  making  the  range  of 
strength  56,000  to  64,000  pounds;  (b)  allows  a  range  from  55,000 
to  65,000  pounds;  (a)  allows  the  same  range  as  (b)  and  in  addition 

*  (a)  Published  in  the  handbooks  issued  by  the  Steel  Manufacturers;  (b>  Published  by 
American  Society  for  Testing  Materials.  Edgar  Marburg,  Secretary,  University  of  Pennsylvania, 
Philadelphia,  Pa.;  published  in  full  in  Carnegie  Steel  Company's  Pocket  Companion,  1913 
edition;  -(e)  Published  by  American  Railway  Engineering  Association,  910  South  Michigan  Boule- 
vard, Chicago,  III. 

t  Class  A  is  for  railroad  bridges. 


44  STEEL  CONSTRUCTION 

permits  a  maximum  of  70,000  pounds  if  the  percentage  of  elongation 
is  the  same  as  for  steel  having  a  tensile  strength  of  65,000  pounds. 

Rivet  Steel  Strength.  Specification  (c)  specifies  the  desired 
strength  of  rivet  steel  at  50,000  pounds,  allowing  4000  pounds  vari- 
ation, thus  making  the  range  of  strength  from  46,000  to  54,000 
pounds;  (a)  allows  a  range  from  46,000  to  56,000  pounds;  and  (b) 
allows  a  range  from  48,000  to  58,000  pounds. 

Elongation  and  Fracture.  The  three  specifications  are  in  close 
agreement  as  to  their  requirements  for  elongation  of  the  test  speci- 
men and  the  character  of  fracture. 

Bending  Requirements.  Specification  (c)  is  somewhat  more 
rigorous  than  the  others  in  the  bending  requirements. 

Either  of  these  specifications  will  give  satisfactory  results,  but 
specification  (b)  of  the  American  Society  for  Testing  Materials  is 
recommended  as  being  most  suitable  for  building  work.  It  is  given 
in  full  on  p.  359. 

DISCUSSION  OF  IMPORTANT  FEATURES 

Method  of  Manufacture.  A  brief  description  has  been  given 
of  the  two  methods  of  manufacture  of  steel.  The  Bessemer  process 
is  more  rapid  and,  as  a  result,  is  less  subject  to  accurate  control  than 
the  open  hearth.  In  the  Bessemer  process  the  operator  is  governed 
by  the  character  and  color  of  the  flame  issuing  from  the  converter. 
He  must  learn  by  experience  to  do  this,  as  the  whole  matter  depends 
upon  his  judgment.  The  open-hearth  process,  being  slower,  gives 
an  opportunity  to  take  samples  and  make  analyses,  and  thus  control 
the  operation. 

The  Bessemer  process,  as  ordinarily  conducted,  does  not  remove 
sulphur  and  phosphorus,  so  that  whatever  quantities  of  these  unde- 
sirable elements  are  in  the  iron  ore  remain  in  the  finished  steel,  On 
the  other  hand,  the  usual  open-hearth  practice  reduces  the  amount 
of  sulphur  and  phosphorus,  these  elements  being  removed  in  the  slag. 

For  the  above  reasons,  the  product  of  the  open-hearth  furnace 
is  considered  more  desirable  than  that  of  the  Bessemer,  when  steel 
is  to  be  subjected  to  severe  use,  as  in  the  case  of  railway  bridges. 

Heretofore  the  question  has  been  an  economic  one.  The  Bes- 
semer process  being  the  cheaper,  most  of  the  producing  capacity 
was  of  that  type,  and  a  higher  price  was  charged  for  open-hearth 


STEEL  CONSTRUCTION  45 

steel.  Recently  the  situation  has  changed.  Most  of  the  new 
furnaces  are  open-hearth  and  no  extra  charge  is  demanded  for  steel 
made  by  this  process.  There  is  now  no  difficulty  in  securing  it. 

Chemical  Composition.  Carbon.  The  essential  elements  of 
steel  are  iron  and  carbon.  All  of  the  other  elements  found  may  be 
considered  as  impurities.  The  iron,  of  course,  constitutes  all  but  a 
small  percentage  of  the  total.  The  function  of  the  carbon  is  to 
make  the  steel  hard  and  strong.  Within  certain  limits  the  tensile 
strength  of  steel  increases,  while  the  ductility  decreases,  with  the 
increase  in  the  amount  of  carbon  used.  The  amount  of  carbon  in 
structural  steel  varies  from  0.10  per  cent  to  0.40  per  cent.  The 
smaller  amount  occurs  in  rivet  steel.  For  structural  shapes,  the 
usual  limits  are  0.15  per  cent  to  0.25  per  cent.  A  larger  amount 
makes  steel  too  hard  for  structural  purposes. 

Steel  to  be  forged  or  welded  needs  to  be  low  in  carbon.  Steel  to 
be  tempered  must  be  high  in  carbon.  These  features  do  not  con- 
cern structural  steel. 

Phosphorus.  Phosphorus  occurs  as  an  impurity  in  the  iron  ore. 
It  is  not  practicable  or  necessary  to  remove  all  of  it.  It  increases 
the  strength  of  the  steel  but  produces  brittleness.  The  amount  of 
phosphorus  allowed  is  about  0.10  per  cent. 

Sulphur.  Sulphur  is  also  found  as  an  impurity  in  the  iron 
ore.  Its  presence  in  the  steel  causes  trouble  in  rolling.  It  usually 
amounts  to  less  than  0.05  per  cent. 

Silicon.  Silicon  may  be  in  the  pig  iron  or  may  be  absorbed 
from  the  material  used  in  lining  the  steel  furnace.  It  increases 
the  hardness  of  the  steel  and  has  a  beneficial  effect  in  the  process  of 
manufacture,  so  that  the  presence  of  a  limited  quantity,  about  0.20 
per  cent,  is  not  objectionable. 

Manganese.  Manganese  also  may  be  found  in  the  iron  ore, 
but  if  not,  it  is  added  during  the  process  of  manufacture  to  assist 
in  the  chemical  transformations.  Its  presence  in  the  finished  steel 
to  the  extent  of  about  1.0  per  cent  is  an  advantage,  as  it  adds  to  the 
strength  and  improves  the  forging  qualities.  However,  some 
authorities  believe  that  it  promotes  corrosion  of  steel  and  on  this 
account  is  objectionable. 

Alloys  of  Steel.  A  much  larger  quantity  of  manganese  is 
sometimes  used  as  an  alloy,  but  such  a  steel  is  not  used  for  structural 


46  STEEL  CONSTRUCTION 

purposes.  There  are  many  alloys  of  steel,  developed  for  special 
purposes.  The  only  one  used  for  structural  work  is  nickel  steel,  and 
up  to  the  present  time  its  use  has  been  limited  to  a  few  large  bridges. 
Probably  nickel  steel  will  not  be  economical  for  building  work  for 
some  time. 

Physical  Properties.  The  determination  of  the  physical  prop- 
erties most  suitable  for  structural  steel  has  been  a  gradual  develop- 
ment. It  has  been  influenced  by  the  cost  of  manufacture  and  ease 
of  fabrication  on  the  one  hand,  and  uniformity  and  economy  to  the 
consumer  on  the  other. 

The  manufacturers  have  required  that  such  limits  be  set  as  would 
permit  them  to  operate  economically.  Expensive  refinements  of 
small  importance  have  been  eliminated.  The  allowable  range  in 
strength  has  been  made  large  enough  so  that  it  can  easily  be  attained. 
The  fabricating  shops  have  encouraged  the  use  of  a  material  that 
can  easily  be  punched  and  sheared. 

The  designing  engineers  representing  the  consumers  have  de- 
manded a  small  range  in  strength  and  uniformity  in  physical  proper- 
ties, and  at  the  same  time  as  great  strength  as  is  consistent  with  relia- 
bility of  material,  with  economy  of  manufacture,  and  with  ease  of 
fabrication. 

As  the  physical  properties  are  closely  related  to  the  uses  of  the 
steel,  their  requirements  are  much  more  explicit  than  are  those 
relating  to  chemical  composition.  The  chemical  tests  are  of  inter- 
est only  to  the  extent  that  they  indicate  physical  properties.  Thus, 
high  carbon  and  high  phosphorus  indicate  high  tensile  strength  and 
brittleness,  but  these  properties  can  be  determined  more  directly  by 
the  tension  test,  with  the  attendant  observations  of  elongation  and 
character  of  fracture. 

Railway  Bridge  Grade  Steel.  It  has  been  noted  that  the  Manu- 
facturers' Standard  Specifications  (a)  provide  for  steel,  which  has 
a  maximum  strength  five  thousand  pounds  greater  than  the  strength 
provided  by  specifications  (b)  and  (c).  This  grade  of  steel  was 
formerly  very  much  used  for  building  work,  but  now  steel  having  the 
lower  strength  is  generally  used.  The  reason  for  using  the  lower 
strength  steel  is  that  it  is  more  reliable  and  more  uniform  in  quality. 
The  higher  the  strength  the  more  brittle  the  material,  hence  the 
greater  danger  of  injury  from  careless  handling  and  from  the  shop 


STEEL  CONSTRUCTION  47 

operations  of  fabricating.  This  latter  condition  makes  the  fabricating 
shops  prefer  to  use  the  softer  grade.  It  seems  probable  that  this 
harder  grade  of  steel  will  be  used  less  and  less  and,  therefore,  more 
difficult  to  get;  so  it  is  wise  to  specify  the  railway  bridge  grade,  which 
is  Class  A,  in  case  Manufacturers'  Standard  Specifications  are  used. 
Yield  Point.  The  yield  point  indicates  one  of  the  most  import- 
ant properties  of  structural  steel.  When  a  piece  of  steel  is  subjected 
to  a  tensile  stress,  it  elongates,  the  amount  of  the  elongation  within 
certain  limits  being  proportional  to  the  load  applied ;  .thus,  if  a  piece  of 
steel  of  one  square  inch  cross  section  is  subjected  to  a  load  of  5000 
pounds,  and  then  to  a  load  of  10,000  pounds,  the  elongation  in  the 
second  case  will  be  twice  as  inuch  as  that  in  the  first  case.  The  test 
for  the  strength  of  the  steel  specimen,  as  described  in  the  specifica- 
tions, is  made  in  a  tension  or  pulling  machine,  to  which  is  attached 
a  lever  arm  carrying  a  weight,  corresponding  to  the  beam  of  an 
ordinary  scale.  If  the  load  is  increased  at  a  uniform  rate,  the 
weight  on  the  scale  beam,  by  being  moved  at  a  certain  uniform 
rate,  will  kee'p  the  beam  exactly  balanced  until  about  one-half  the 
ultimate  strength  of  the  material  is  reached;  then  the  scale  beam 
will  drop,  which  indicates  that  the  specimen  has  begun  to  elongate 
at  a  more  rapid  rate.  The  stress  in  the  steel  at  which  this  occurs 
is  called  the  "yield  point"  of  the  steel. 

Breaking  Load.  If  the  load  which  produced  the  above  effect  were 
applied  continuously  for  a  long  time,  the  specimen  would  finally 
break;  but  usually  in  testing,  additional  load  is  applied  at  the 
same  rate  as  before  until  the  specimen  breaks.  The  breaking  load, 
according  to  the  specifications,  should  be  about  60,000  pounds  per 
square  inch.  This  represents  the  load  which  will  break  the  steel  if 
applied  within  a  relatively  brief  period  of  time,  but  a  much  smaller 
load  will  break  it  if  applied  over  a  long  period  of  time. 

Elastic  Limit.  The  change  in  the  rate  of  elongation  does  not 
occur  just  at  the  point  where  it  becomes  manifest  by  the  action  of 
the  scale  beam,  but  at  a  somewhat  lower  stress.  The  point  where 
the  change  actually  occurs  is  called  the  "elastic  limit".  This  term 
formerly  was  used  in  specifications  and,  in  fact,  still  is  used  in  the 
Manufacturers'  Standard  Specifications,  but  as  the  commercial 
methods  of  testing  structural  steel  do  not  clearly  show  the  exact 
point  of  the  elastic  limit,  the  yield  point  is  u§ed. 


48  STEEL  CONSTRUCTION 

Yield  Point  and  Factor  of  Safety.  The  Standard  Specifications 
require  that  the  yield  point  shall  be  not  less  than  one-half  the  ulti- 
mate strength.  The  value  of  the  yield  point  is  usually  several 
thousand  pounds  above  this  amount.  When  the  yield  point  is 
reached,  the  material  has  begun  to  fail.  This  value,  therefore,  in- 
stead of  that  for  the  ultimate  strength,  is  the  one  which  should  be 
used  in  computing  the  factor  of  safety.  If  the  yield  point  is  at  32,000 
pounds  and  the  unit  stress  16,000  pounds,  the  factor  of  safety  is  2 
instead  of  4,  as  commonly  stated.  Refer  to  the  discussion  of 
factor  of  safety,  p.  7. 

Reduction  of  Area.  The  provision  in  the  specifications  re- 
garding the  reduction  of  area  of  the  test  piece  at  the  point 
of  fracture  is  of  importance,  as  it  indicates  the  ductility  of  the  metal. 
If  the  piece  breaks  without  much  reduction  in  area,  it  indicates  that 
the  material  is  hard  and  probably  brittle.  Such  material  is  likely 
to  break,  if  subjected  to  shock,  and  may 

/" —  *7  Jd  ~  ZZ?  fracture  in  punching  and  shearing  The 
yj  — \  character  of  the  fracture  is  indicative  of  the 

FOP  STRUCTURAL  STCLL  same  condition.  If  cup-shaped  and  silky  in 
(^  — ^  appearance,  it  indicates  toughness;  but  if  the 

roR  PH/CT  STEEL  fracture  is  irregular,  it  indicates  brittleness. 

Fig.  45.  Biding  Tests  for  The  bending  test  also  is  importantTor  deter- 
mining whether  the  steel  is  tough  or  brittle. 

Inspection  and  Tests.  In  order  to  check  the  quality  of  the 
steel  as  it  is  made,  tests  are  made  of  each  melt.  The  chemical 
analysis  is  made  from  a  sample  taken  from  the  molten  metal  as  it 
comes  from  the  furnace  or  converter.  Sometimes  a  check  analysis 
is  made  from  drillings  taken  from  the  rolled  sections. 

Physical  tests  are  made  in  accordance  with  the  requirements  of 
the  standard  specifications.  The  test  specimens  are  cut  from  the 
finished  structural  steel.  The  bend  test  is  made  by  bending  the 
specimen  around  a  pin  whose  diameter  equals  the  thickness  of  the 
specimen,  Fig.  45.  Rivet  rods  must  bend  flat  on  themselves.  These 
tests  are  made  with  cold  steel.  The  work  is  done  either  by  blows 
or  by  pressure.  To  pass  the  test,  the  specimens  must  show  no 
fracture  on  the  outside  of  the  bent  portion. 

The  tension-test  specimen  is  shaped  as  shown  in  Fig.  46.  It  is 
put  in  a  tension-testing  machine  and  pulled  until  it  breaks.  From 


STEEL  CONSTRUCTION 


49 


this  are  determined  the  total  strength,  yield  point,  elongation,  and 
character  of  fracture,  Fig.  47. 

Records  of  these  tests  are  furnished  to  customers  if  desired. 


/  "TO  j  "/?/?£ 

HOT  L£SS    THfJH  9" 

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} 

\ 
ABOUT  £ 

1 

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£TC. 

ABOUT  /8  ~ 

Fig.  46.     Tension  Test  Piece 


Customers  may,  and  on  important  jobs  do,  employ  inspectors  to 
supervise  the  tests.  These  inspectors  also  make  a  surface  inspection 
to  see  that  the  finished  sections  are  straight  and  free  from  cracks, 
blisters,  buckles,  and  slivers.  Fig.  48  is  a  specimen  report  of  tests. 


Fig.  47.     Test  Piece  Before  and  After  Being  Broken  by  Tension 


UNIT  STRESSES 

General  Discussion.  The  unit  stress,  or  working  stress,  is  the 
stress  or  load  that  is  allowed  on  each  square  inch  of  cross  section  of 
the  metal  and  is  expressed  in  pounds  per  square  inch.  There  is 


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STEEL  CONSTRUCTION  51 

practical  agreement  on  the  values  used  for  the  various  kinds  of 
stress.  The  following  values  can  be  used  with  assurance  that  they 
will  give  safe  results.  Note  that  these  values  are  for  building  work; 
they  may  also  be  used  for  highway  bridges  but  not  for  railroad 
bridges. 

Structural  Steel.  Structural  steel  is  so  dependable  and  of  such 
uniform  quality  that  the  values  for  unit  stress  are  well  established. 
The  values  given  follow  standard  practice. 

Maximum  Allowable  Stresses  on  Structural  Steel  in  Pounds  per 
Square  Inch: 

Axial  tension  net  section 16,000 

Bending  on  extreme  fiber,  tension 16,000 

Bending. on  extreme  fiber,  compression 16,000 

Bending  on  extreme  fiber,  of  pins... 25,000 

Shear  on  shop-driven  rivets 12,000 

Shear  on  field-driven  rivets  and  turned  bolts 10,000 

Shear  on  rolled-steel  shapes 12,000 

Shear  on  plate-girder  webs 10,000 

Bearing  on  shop-driven  rivets  and  pins 25,000 

Bearing  on  field-driven  rivets  and  turned  bolts 20,000 

Axial  compression  on  columns 16,000  —  70  — 

In  the  above,  /  is  the  length  of  the  column  in  inches  from  center  to 
center  of  bearing,  and  r  is  the  least  radius  of  gyration.  The  maxi- 
mum value  allowed  is  14,000  pounds  per  square  inch. 

For  wind  pressure  alone  or  combined  with  gravity  loads,  the 
unit  stresses  may  be  50  per  cent  in  excess  of  those  given  above,  but 
the  section  must  not  be  less  than  required  for  the  gravity  loads  alone. 

The  discussion  under  "Columns"  should  be  consulted  regarding 
limitations  of  the  use  of  the  compression  formula  and  the  conditions 
under  which  higher  and  lower  values  are  used. 

Cast  Iron.  There  is  not  such  close  agreement  among  engineers 
as  to  the  unit  stresses  allowable  on  cast  iron.  The  following  values 
represent  fairly  well  the  current  practice;  they  are  in  pounds  per 
square  inch. 

Axial  tension not  allowed 

Bending  on  extreme  fiber,  tension 3,000 

Bending  on  extreme  fiber,  compression 10,000 

Shear 2,000 

Compression 10,000-6o| 


52  STEEL  CONSTRUCTION 

The  discussion  of  cast-iron  columns  should  be  consulted  for 
limitations  of  values  used  and  length  of  columns.  These  values  are 
taken  from  the  Building  Ordinances  of  the  City  of  Chicago. 

Masonry.  As  the  ultimate  bearing  of  steel  work  is  on  masonry, 
and  as  the  bearing  values  are  necessary  in  designing  the  bearing 
plates  and  column  bases,  the  values  are  given  for  the  usual  forms  of 
masonry.  The  values  below,  expressed  in  pounds  per  square  inch, 
are  taken  from  the  Building  Ordinances  of  the  City  of  Chicago. 

Coursed  rubble,  Portland  cement  mortar 200 

Ordinary  rubble,  Portland  cement  mortar 100 

Coursed  rubble,  lime  mortar 120 

Ordinary  rubble,  lime  mortar GO 

First-class  granite  masonry,  Portland  cement  mortar 600 

First-class  lime  and  sandstone  masonry,  Portland  cement 

mortar 400 

Portland  cement  concrete,  -2-4  mixture,  machine  mixed 400 

Portland  cement  concrete,  -2-4  mixture,  hand  mixed 350 

Portland  cement  concrete,  -2^-5  mixture,  machine  mixed. . .  350 

Portland  cement  concrete,  -2J/2-5  mixture,  hand  mixed 300 

Portland  cement  concrete,  -3-6  mixture,  machine  mixed 300 

Portland  cement  concrete,  1-3-6  mixture,  hand  mixed 250 

Natural  cement  concrete,  1-2-5  mixture ;  150 

Paving  brick,  mortar  1  part  Portland  cement,  3  parts  torpedo 

sand 350 

Pressed  brick  and  sewer  brick,  mortar  same  as  above 250 

Hard  common  select  brick,  same  as  above 200 

Hard  common  select  brick,  mortar,  1  part  Portland  cement, 

1  part  lime,  3  parts  sand 175 

Common  brick,  all  grades,  Portland  cement  mortar 175 

Common  brick,  all  grades,  good  lime  and  cement  mortar  .  .  .  125 

Common  brick,  all  grades,  natural  cement  mortar 1,50 

Common  brick,  all  grades,  good  lime  mortar 100 

The  American  Railway  Engineering  Association  permits  a 
bearing  of  800  pounds  per  square  inch  on  concrete,  provided  the 
area  of  the  pier  is  twice  the  area  of  the  base  plate.  The  writer 
would  allow  this  high  stress  only  when  the  concrete  is  properly 
reinforced  with  hooping,  similar  to  that  used  in  hooped  columns. 

RIVETS  AND  BOLTS 

Ordinary  Sizes.  The  sizes  of  rivets  vary  in  a  general  way  with 
the  thickness  of  steel  which  they  connect.  In  structural  steel  work 
the  sizes  commonly  used  are  |  inch,  \  inch,  and  J  inch,  the  f-inch 


STEEL  CONSTRUCTION  53 

size  being  used  much  more  than  any  other.  In  very  light  work 
s-inch  rivets  are  sometimes  used  and,  in  very  heavy  work,  rivets  1 
inch,  1J  inches,  and  1J  inches  are  used. 

Rivets  smaller  than  J  inch  are  used  when  the  size  of  the  mem- 
bers connected  requires  it,  or  when  the  thickness  of  metal  used  is 
chiefly  J  inch.  |-inch  rivets  must  be  used  in  the  flanges  of  6-inch 
and  7-inch  I-beams;  6-inch  and  7-inch  channels;  and  2-inch  angles, 
f-inch  rivets  can  be  used  in  all  of  the  beams,  channels,  and  angles 
larger  than  the  above'  sizes,  {-inch  rivets  may  be  used  in  beams 
18  inches  and  larger,  and  angles  3  inches  and  larger. 

Another  consideration  that  sometimes  affects  the  sizes  of  rivets 
used,  and  concerns  particularly  the  sizes  larger  than  J  inch,  is  the 
thickness  of  metal  to  be  joined  together.  It  is  the  general  experi- 
ence in  shops  that  satisfactory  punching  cannot  be  done  when  the 
thickness  of  metal  is  greater  than  the  diameter  of  the  hole  to  be 
punched.  Of  course,  it  is  possible  to  punch  thicker  material  than 
this,  but  it  is  troublesome  to  do  so  because  of  the  frequent  breakage 
of  punches.  Consequently  if  most  of  the  material  to  be  punched  is 
J  inch  in  thickness,  J-inch  rivets  will  be  used. 

Another  approximate  rule  governing  the  size  of  rivets  is  that  in 
general  the  diameter  of  the  rivet  shall  be  not  less  than  one-fourth  of 
the  total  thickness  of  metal. 

The  use  of  more  than  one  size  of  rivet  on  a  job  is  to  be  avoided 
as  much  as  practicable  on  account  of  the  trouble  and  expense  of 
frequently  changing  the  punches.  It  is  especially  inconvenient  to 
punch  more  than  one  size  of  hole  or  drive  more  than  one  size  of  rivet 
in  a  structural  member. 

Spacing.  There  are  a  number  of  conditions  that  control  the 
spacing  of  rivets.  These  have  been  developed  into  practical  rules 
which  are  quite  uniform  among  the  various  fabricating  shops. 
Rivets  spaced  too  close  together  would  cut  out  too  large  a  percentage 
of  the  cross  section  of  members.  Rivets  spaced  too  far  apart  cause 
a  waste  of  material  in  connecting  pieces. 

The  specifications  relating  to  rivet  spacing,*  p.  365,  items  57 
to  63,  are  in  accord  with  usual  practice  and  should  be  followed. 


*Frora  "Specifications  for  Structural  Work  of  Buildings"  by  C.  C.  Schneider,  M.  Am.  Soc. 
C.  E.,  published  in  Transactions  of  the  American  Society  of  Civil  Engineers,  Vol.  LIV  (June,  1905), 
p.  498. 


54 


STEEL  CONSTRUCTION 


TABLE  I 
Gages  for  Angles 


p\ 

Leg 

3  i 

t 

s, 

i 

g  ] 

G, 

§; 

3* 
3" 

CO  tO  4^ 

to  toco 

3" 

2'» 

2f 

2" 

If 

.  *  T*  T 

Max.  Rivet 

lf 

1" 

i" 

i1 

i 

5 

| 

Leg 

2f 

2" 

If 

if 

if 

if 

i" 

f 

Gt 

G2 

if 

If 

1" 

8 

i" 

i" 

i" 

f 

G, 

Max.  Rivet 

i; 

I 

f 

1" 

I" 

t" 

i" 

i" 

Gage.  The  term  "gage"  is  used  to  designate  the  spacing  of 
rivet  lines  parallel  to  the  axis  of  the  member.  For  example, 
Fig.  49  illustrates  the  gage  lines  of  beams,  channels,  and  angles. 
Standard  values  are  assigned  in  the  hand-books  to  the  gage  lines  in 
the  flanges  of  I-beams  and  channels,  and  in  angles.  However,  as 
manufacturers  do  not  agree  as  to  the  gage  lines  of  angles,  values 
used  by  the  American  Bridge  Company  are  given,  Table  I. 

Gage  lines  in  webs  of  beams  and  channels  and  in  plates  are  not 
standard  and  are  located  according  to  requirements. 


GAGE 
LINES 


Fig.  49.     Diagrams  Showing  Gage  and  Pitch  Lines 

Pitch.  By  the  pitch  of  rivets  is  meant  the  spacing  along  the 
gage  lines,  Fig.  49.  Some  of  the  rules  for  this  spacing  are  given  in 
Schneider's  Specifications  previously  referred  to.  Note  carefully 


STEEL  CONSTRUCTION  55 

the  provisions  there  given.  The  rule  usually  followed  for  the  mini- 
mum pitch  is  three  times  the  diameter  of  the  rivet.  But  this  mini- 
mum should  be  used  only  when  necessary,  it  being  preferable  to  use 
a  larger  spacing  of  rivets  under  ordinary  conditions.  Three  inches 
is  desirable  for  f-inch  rivets,  where  this  spacing  does  not  involve 
the  use  of  an  excess  of  material  in  the  connected  pieces.  Where  no 
definite  stress  occurs  in  the  rivet,  as  in  built-up  columns,  or  where 
the  stress  is  small,  as  in  certain  portions  of  flanges  of  plate  girders, 
six  inches  has  been  established  as  the  maximum.  In  case  there  are 
two  gage  lines  closer  together  than  the  minimum  spacing  allowed,  the 
rivets  in  the  adjacent  rows  must  alternate  so  that  the  diagonal  dis- 
tance between  them  will  exceed  the  minimum  by  40  per  cent  or 
more. 

Edge  Distance.  If  holes  are  punched  too  close  to  the  edge  of 
the  metal,  the  tendency  is  to  bulge  out  the  metal  and  perhaps  to 
crack  the  edge.  This  necessitates  maintaining  a  certain  distance 
fpom  the  edge  to  the  center  of  the  rivet  holes.  This  distance  must 
be  greater  in  the  case  of  a  sheared  edge,  as  of  a  plate,  than  is  required 
for  a  rolled  edge,  as  the  flange  of  a  beam,  an  angle,  or  a  universal 
mill  plate.  The  values  commonly  used  are  given  in  Schneider's 
Specifications  quoted  above. 

In  the  smaller  sizes  of  beams  and  channels,  the  gage  distances 
do  not  comply  with  these  specifications.  The  width  of  flange  is 
not  sufficient  to  permit  the  use  of  the  full  edge  distance  and  still 
allow  necessary  clearance  from  web  to  permit  driving.  On  account 
of  the  danger  that  the  metal  will  bulge  out  or  crack  along  the  edge, 
designers  should  try  to  avoid  using  smaller  than  10-inch  I-beams  and 
channels  in  a  way  that  will  require  flange  punching.  Instead, 
web  connections  or  clips  and  clamps  can  generally  be  used. 

Clearance,  A  hole  cannot  be  punched  close  against  the  web  of 
an  I-beam  or  close  to  the  leg  of  an  angle.  A  certain  amount  of 
space  is  required  for  the  die.  Of  course  holes  can  be  drilled  in  any 
position,  but  this  is  not  resorted  to  unless  there  is  some  particular 
reason  for  so  doing.  However,  the  punching  of  holes  is  not  the 
limiting  feature  in  the  matter  of  rivet  clearance.  The  required 
clearance  is  governed  by  the  size  of  the  die  used  in  forming  the  rivet 
head.  The  usual  rule  for  clearance  is  one-half  the  diameter  of  the 
rivet  head  plus  three-eighth  of  an  inch.  The  clearances  required  for 


56 


STEEL  CONSTRUCTION 


various  conditions  for  several  sizes  of  rivets  are  given  in  Fig.  50, 
which  represents  the  practice  of  the  American  Bridge  Company. 

Closely  associated  with  the 
amount  of  clearance  is  the  ac- 
cessibility for  driving  the  rivets, 
Fig.  51.  For  power  driving,  the 
rivet  must  be  so  situated  that  it 
can  be  brought  between  the  jaws 
of  the  riveting  machine.  For 
riveting  with  the  percussion  ham- 
mer (air  hammer),  it  must  be 
possible  to  hold  on  to  one  head 
of  the  rivet  with  a  die  while  the 
other  head  is  formed  by  the  riv- 
eter. For  hand  riveting  it  is 
necessary  to  be  able  to  hold  on  to  one  head  of  the  rivet  and 
that  the  other  end  of  it  be  accessible  for  driving  with  a  maul. 
It  is  sometimes  necessary  to  cut  away  flanges  of  I-beams  or  cut 
holes  in  the  webs  of  box  girders  to  make  the  rivets  accessible  for 
driving,  Fig.  51.  This  matter  is  generally  looked  after  in  making 
shop  drawings,  but  needs  some  attention  in  designing. 


H  

^  £1^ 

L.     . 
V 

J 

J       .-_  i 

M1N, 

STD. 

r. 

>*;. 

FOK  /  f  KJVZTS 

i 

/3 

"          4                " 

*l  » 

*t 

I  "          " 

*4 

1  1  " 

/  "             >t 

'i~ 

'i" 

"         //'            " 

Fig.  50.     Clearance  Allowed  for  Riveting 

9 — a 


USUAL    METHOD 


IMPOSSIBLE:  TO 
DRIVC  BY 

USUAL   METHODS 


rLAHGE   Or  BEAMS 
CUT  AWAY  TO 
PERMIT  DRIVIHG 


f>  RIVETS  CAfiHOT 

-  BE  DRIVEM  AFTER 

BEAMS   ARE 

ASSEMBLED 


Fig.  51.     Difficult  Situations  for  Riveting 


Rivet  Heads.  Manufacture.  Rivets  are  made  with  one  head. 
This  is  done  by  heating  a  length  of  rivet  rod  to  the  proper  tempera- 
ture and  running  it  into  the  rivet  machine.  The  machine  upsets 
the  end  of  the  rod,  making  a  head,  and  then  cuts" off  the  rivet  to  the 
desired  length.  It  is  necessary  that  the  dies  in  which  the  heads 
are  formed  be  of  proper  size  and  be  kept  in  perfect  condition  in  order 
to  make  good  rivets.  If  the  two  halves  of  the  die  which  grip  the 
sides  of  the  rivet  do  not  fit  closely,  some  of  the  metal  will  be  forced 


STEEL  CONSTRUCTION 


57 


between  them,  forming  fins  on  the  sides  of  the  rivets,  Fig.  52.    If 
the  corners  of  the  die  become  rounded,  a  shoulder  wiU  be  formed  at 
the  junction  of  the  shank  with 
the  head.    Either  of  these  de- 
fects will  prevent  the  rivet  head 
from  fitting  up  tight  against  the 
plate,   thus   causing   unsatisfac- 
tory results  when  driven.    This  Fig.  62.   Defective  Rivets 
point  is  especially  important  in 
tank  work  where  the  rivets  must  be  water-tight. 

Button  Head.  The  shapes  of  the  rivet  heads  vary  among 
different  makers,  although  these  variations  are  slight.  The  type 
of  head  used  in  structural  work  is  called  the  "button  head"  to  dis- 
tinguish it  from  the  cone  head  which  is  used  in  tank  and  boiler  work. 

Flattened  and  Countersunk  Heads.  It  is  sometimes  necessary 
to  flatten  rivet  heads  for  special  situations  in  order  to  provide  the 
required  clearance  for  an  adjacent  member.  This  flattening  may 
vary  from  a  slight  reduction  from  the  full  thickness  of  the  head 
down  to  a  flush  or  countersunk  head.  The  different  thicknesses 
ordinarily  used  are  f  inch,  J  inch  and  |  inch.  A  countersunk  rivet 
is  one  in  which  the  head  is  made  in  the  form  of  a  truncated  cone  and 
is  formed  by  driving  in  a  hole  which  has  been  tapered  by  reaming 


FORMULAE 

-dXt5+£  a-DiAM.  OF  HEAD 

-a*   4ZS  b -HEIGHT 

-i>  X I  f  e.-i-  ONO  RADIUS 

-b  •          c 'SHORT  RADIUS 


Diam. 

of 
Rivets 


Diam. 

of 
Holes 


FULL  DRIVEN  HEAD 


Height 


COUNTERSUNK 


Depth 


H 


15 

I 


If 


Fig.  53.     Proportions  of  Rivets  in  Inches 
Prom  American  Bridge  Company 


58  STEEL  CONSTRUCTION 

so  that  the  diameter  at  the  outside  is  greater  than  at  the  inside  of 
the  plate.  The  sizes  of  rivet  heads  are  shown  in  Fig.  53.  The 
conventional  signs  for  riveting  are  given  in  the  handbooks. 

It  is  to  be  noted  that  countersunk  rivets  are  not  as  strong  as 
rivets  with  button  heads  and  are  much  more  expensive,  conse- 
quently they  are  not  used  unless  absolutely  required  by  the  condi- 


Fig.  54.     100-Ton  Hydraulic  Riveter,  120-inch  Gap 
Courtesy  Mackintosh,  Hemphill  &  Company 

tions.  A  flattened  rivet  should  be  used  in  preference  to  a  counter- 
sunk rivet;  but  when  a  smooth  surface  is  to  be  obtained,  the  head 
must  be  countersunk  and  chipped  flush  with  the  plate. 

Driving.  Before  rivets  can  be  driven,  the  pieces  to  be  joined 
must  be  assembled  accurately  in  position  and  be  held  together  with 
bolts.  The  number  of  bolts  used  for  this  purpose  will  depend  to 


STEEL  CONSTRUCTION 


59 


some  extent  on  the  accuracy  of  the  punching  and  the  straightness  of 
the  pieces.  If  the  several  pieces  are  not  held  together,  the  metal  of 
the  rivet  will  be  forced  out  between  them,  or  the  driving  of  adjacent 


Fig.  55.     Hanna  Pneumatic  Riveter,  24-inch  Gap 
Courtesy  Vulcan  Engineering  Sales  Company 


rivets  may  draw  the  plates  closer  together 
previously  driven. 

Rivet  holes  are  punched  A  inch  larger 
of  the  rivet  for  when  the  rivet  is  heated, 
making  it  necessary  to  have  the  larger  size 
the  rivet  must  be  done  in  such  a  way  as  to 
shank  so  that  it  fills  the  rivet  hole  solidly, 
filling  out  any  irregularities  in  the  hole,  and 


and  loosen  the  rivets 

than  the  nominal  size 
it  expands  somewhat, 
hole.  The  driving  of 
upset  the  metal  of  the 
even  to  the  extent  of 
then  the  button  head 


60 


STEEL  CONSTRUCTION 


must  be  formed  on  the  driving  side.    As  the  rivet  cools,  it  shrinks 
and  thus  grips  the  steel  more  tightly. than  when  first  driven. 


Fig.  56.     Rivet  Ready  for  Driving 
Courtesy  Vulcan  Engineering  Sales  Company 


Riveting  Machines  in  Shop.    In  the  shop,  rivets  are  driven  with 
an  hydraulic  riveter,  Fig.  54,  or  a  pneumatic  riveter,  Fig.  55.    The 


Fig.  57.     Three  Stages  in  Process  of  Riveting 

machine  consists  essentially  of  a  yoke  which  spans  the  members 
to  be  riveted,  Fig.  56.    On  the  outer  arm  of  the  yoke  is  a  die  which 


STEEL  CONSTRUCTION  Gl 

fits  over  the  head  of  the  rivet;  the  other  arm  carries  a  similar  die, 
or  rivet  set,  which  pushes  against  the  end  of  the  rivet,  upsetting  the 
shank  of  the  rivet  and  thus  forming  a  head,  Fig.  57  The  power  is 
applied  by  means  of  hydraulic  or  pneumatic  pressure.  The  pressure 


Fig.  58.     Pneumatic  Riveting  Hammer 
Courtesy  Chicago  Pneumatic  Tool  Comjtany 

is  held  on  until  the  rivet  is  partly  cooled  and  has  acquired  enough 
strength  so  that  the  spring  of  the  plates  will  not  stretch  it. 

Pneumatic  Hammer.    Whenever  the  rivet  is  in  such  position 
that  it  cannot  be  reached  by  means  of  the  power  riveter,  it  is  driven 


Fig.  59.     Light  Motor-Driven  Punch 
Ctmrteay  Mackintosh.  Hemphill  &  Company 

with  a  pneumatic  hammer.  The  rivet  is  inserted  in  the  hole  and 
held  in  place  by  means  of  a  die  pressed  against  the  head,  the  die 
being  -held  in  position  by  hand  or  by  a  suitable  arrangement  of 
levers.  The  pneumatic  riveter,  or  air  gun,  Fig.  58,  carries  a  die, 


62 


STEEL  CONSTRUCTION 


or  set,  for  upsetting  the  rivet  and  forming  the  head.  When  the 
power  is  turned  on,  this  machine  delivers  very  rapid  blows  and  thus 
performs  the  required  work.  Riveting  in  the  field  on  the  assembled 
structure  is  usually  done  by  means  of  the  pneumatic  hammer. 

Hand  Riveting.  Hand  riveting  is  now  used  only  on  small  jobs, 
the  air  gun  being  replaced  by  the  sledge  hammer.  The  rivet  is 
first  hammered  down  by  blows  from  the  sledges,  then  the-  rivet 
set  is  applied  and  sledged  to  form  the  head  to  its  proper  shape. 

Perfect  rivets  can  be  driven  by  either  of  the  above  methods. 


Fig.  GO.     Heavy  Motor-Driven  Multiple  Punch 
Courtesy  of  Mackintosh,  Hemphill  &  Company 


Punching  and  Reaming.  Rivet  holes  in  structural  steel  work 
are  ordinarily  punched  in  the  metal  by  means  of  a  powerful  punching 
machine,  Figs.  59  and  GO  showing  examples  of  the  single  and  multi- 
ple types,  respectively.  The  essential  features  of  the  machine  for 
doing  this  work  are  a  punch  and  a  die.  The  die  is  usually  about 
A  inch  larger  in  diameter  than  the  punch.  The  two  are  placed 


STEEL  CONSTRUCTION  63 

in  the  machine  so  that  their  axes  are  exactly  in  line.  The 
plate  is  placed  over  the  die  and  the  punch  is  forced  through,  thus 
shearing  out  a  round  piece.  This  resulting  hole  is  not  perfectly 
smooth.  The  degree  of  roughness  will  depend  on  the  condition  of 
the  punch  and  die,  and  the  amount  of  difference  in  their  diam- 
eters. The  metal  around  the  hole  is  to  some  extent  torn  and 
distorted. 

For  ordinary  structural  purposes  the  holes  are  accurate  enough 
and  the  damage  to  the  metal  so  slight  that  no  further  treatment  is 
needed,  but  in  railroad  structures  and  sometimes  for  special  cases 
of  building  work  it  is  required  that  the  holes  be  reamed.  In  such 
cases  the  hole  is  punched  smaller  than  the  size  of  the  rivet — called 
"sub-punching" — and  it  is  then  enlarged  to  the  proper  size  by 
means  of  a  drill  or  reamer.  In  railroad  bridge  construction,  it  is 
customary  to  ream  all  metal  over  f  inch  in  thickness  and  to  ream 
all  holes  for  field  connections.  In  structural  work  for  buildings, 
reaming  is  rot  required  to  such  a  great  extent.  Sometimes  it  is 
required  on  metal  thicker  than  f  inch  and  on  field  connections  of 
very  heavy  members  where  a  slight  inaccuracy  would  occasion 
serious  inconvenience  in  erecting. 

Where  the  several  pieces  assembled  together  have  a  thickness 
of  more  than  four  times  the  diameter  of  the  rivet,  or  where  through 
any  inaccuracy  of  punching  the  holes  do  not  match  accurately,  the 
holes  should  be  reamed  to  true  them  up ;  but  in  such  cases  they  need 
not  be  sub-punched  and  the. reaming  only  serves  the  purpose  of 
trimming  up  the  irregularities. 

As  previously  stated,  the  diameter  of  the  rivet  hole  as  punched 
is  A  inch  larger  than  the  diameter  of  the  rivet ;  but  in  order  to  take 
account  of  the  injured  metal  in  computing  the  net  section,  the  hole 
is  figured  J  inch  larger  than  the  rivet. 

Functions  of  Rivets  and  Bolts.  Rivets  and  bolts  are  used  for 
fastening  together  the  several  sections  used  in  building  up  the 
structural  steel  members  and  for  connecting  the  members  together 
in  the  finished  structure.  Rivets  are  always  used  for  this  purpose 
unless  there  is  some  special  reason  for  using  bolts.  Generally 
speaking,  rivets  are  cheaper  than  bolts  and  for  most  purposes  more 
effective.  They  fill  the  holes  full  even  though  the  holes  may  be 
slightly  irregular  in  shape,  and  if  driven  tight  will  remain  so;  whereas 


64 


STEEL  CONSTRUCTION 


bolts,  unless  they  are  turned  and  driven  tight  into  reamed  holes, 
are  apt  to  become  loose  after  a  time. 

The  function  of  rivets  is  to  hold  one  piece  of  steel  to  another 
and  to  transmit  stress  from  one  to  the  other.  In  so  doing  they 
must  resist  a  bearing  pressure  and  a  shearing  stress. 

In  many  cases  the  rivets  are  not  subjected  to  any  definite  shear- 
ing or  bearing  stress,  but  simply  serve  to  hold  the  steel  sections 
together  in  built-up  members.  They  are  unquestionably  subjected 
to  some  stresses,  but  it  is  not  possible  to  determine  just  what  these 
are.  In  such 'situations  the  spacing  of  rivets  is  governed  by  rules 
resulting  from  practical  experience. 

It  sometimes  happens  that  the  direction  of  the  stress  applied 
to  the  rivet  is  along  its  axis,  that  is,  the  rivet  is  subjected  to  tension. 
It  was  formerly  the  custom  to  specify  that  rivets  should  not  be 


9? 


Fig.  61.     Diagrams  Showing  Stresses  in  Rivets 

subjected  to  tension,  but  that  bolts  should  be  used  in  such  situations. 
This  provision  was  necessary  when  wrought-iron  rivets  were  in  use, 
as  their  heads  could  be  easily  broken  off.  Steel  rivets  are  much 
more  reliable  in  this  respect  and,  if  properly  driven,  can  be  sub- 
jected to  tension  as  safely  as  bolts. 

Bearing.  Fig.  61-a  represents  two  pieces,  m  and  n,  riveted 
together,  so  that  the  stress  (4000  pounds)  in  m  is  transmitted  to  n. 
Fig.  61-b  represents  three  pieces  riveted  together  so  that  the  stress 
(8000  pounds)  in  the  center  piece  m  is  transmitted  to  the  two  out- 
side pieces  I  and  n. 

The  bearing  on  the  rivet  is  the  pressure  exerted  on  it  by  the 
plate  through  which  it  passes.  In  Fig.  61-a  the  bearing  from  plate 
m  is  on  the  right  half  of  the  rivet  and  from  plate  n  on.  the  left  half 
of  the  rivet.  Although  the  actual  bearing  is  on  the  curved  surface, 


STEEL  CONSTRUCTION  65 

i.  e.,  one-half  the  circumference  of  the  rivet,  the  area  used  in  figuring 
is  the  projected  area  of  this  surface,  i.  e.,  the  thickness  of  the  plate 
multiplied  by  the  diameter  of  the  rivet.  For  the  plate  ra,  the  area 
is  J" X  J*  or  .375  sq.  in.,  and  for  plate  n,  f'X  J"  or  .281  sq.  in. 

The  unit  stress  allowed  in  bearing  is  25,000  pounds  per  square 
inch  for  shop-driven  rivets;  thus  the  allowed  values  in  bearing  are 

for  m         0.375  X  25,000  =  9375  # 

for  n          0.281  X  25,000  =  7025  # 

The  stress  actually  transmitted  is  4000  pounds,  and  each  bearing  must 
be  good  for  at  least  this  amount,  hence  the  bearings  are  sufficient. 
The  actual  bearings  per  square  inch  are 

form          4000  ^0.375  =  10,600  # 

for  n  4000-^0.281  =  14,200  # 

PROBLEM 

Compute  from  the  above  data  the  allowable  bearing  values  for  m  and  n  and 
the  actual  bearing  per  square  inch  on  m  and  n  for  field-driven  rivets. 

In  Fig.  61-b  the  stress  is  transmitted  from  the  plate  m  to  the 
plates  /  and  n  and  divided  equally  between  them.  The  bearing 
areas  are 

form  ¥x¥        =  0.375  sq.  in. 

for  I  and  n  combined    2  Xf  Xf  =  0.5625  s<|.  in. 
,  The  allowed  bearing  values  on  shop-driven  rivets  are 

form  0.375  X 25,000=    9375 # 

for  I  and  n  combined    0.5625  X  25,000  =  14,065  # 
The  stress  actually  transmitted  is  8000  pounds,  so  that  the  bearing 
for  m  is  8000  pounds  and  for  I  and  n  4000  pounds  each;  hence,  the 
bearings  are  sufficient. 

The  actual  bearings  per  square  inch  are 

form  8000^0.375   =21,300# 

for  /  and  n  combined    8000^ 0.5625  =  14,200# 
PROBLEM 

Compute  from  the  above  data  the  allowable  bearings  for  I,  m,  and  n  for 
field-driven  rivets. 

Shear.  Referring  again  to  Fig.  61-a,  the  forces  acting  on  the 
two  plates  tend  to  cut,  or  shear,  the  rivet  along  the  plane  between 
the  plates.  This  shearing  action  is  resisted  by  the  cross-section 

area  of  the  rivets.    This  sectional  area  is  -—,  which  in  this  case  is 


66  STEEL  CONSTRUCTION 

-I-T—  X|Xf  or  0.4418  sq.  in.     The  unit  stress  allowed  fn  shear 

on  shop-driven  rivets  is  12,000  pounds  per  square  inch.  Then  the 
allowable  value  for  one  f-inch  rivet  is  12,000x0.4418  or  5302.  This 
is  greater  than  the  actual  stress  applied  and  is  sufficient. 

The  actual  shear  on  the  rivet  per  square  inch  of  cross  section  is 

4000-4-0.  4418  =  9054$ 
PROBLEM 

Compute  the  shearing  value  of  a  f-inch  rivet,  field  driven. 

In  Fig.  61-b  there  is  a  tendency  to  shear  the  rivet  along  two 
planes,  i.  e.,  on  each  side  of  the  plate  m.  Consequently  the  shearing 
value  of  one  rivet  in  this  case  is  twice  the  value  computed  above,  or 
2X5302  or  10,604  pounds,  and  is  sufficient  to  carry  the  actual  load, 
which  is  8000  pounds.  The  actual  shear  per  square  inch  is  the 
same  as  before,  because  both  the  actual  load  and  the  total  cross- 
section  area  resisting  it  are  twice  as  much  as  before,  giving 
8000^(2X0.4418)  =  9054# 

In  the  first  case  the  rivet  is  in  single  shear,  in  the  second  case 
i&.-is  in  double  shear.  It  is  clear  that  rivets  should  be  used  in 
cldtible  shear  wherever  possible,  provided  the  middle  plate  has  a 
bearing  value  more  than  that  of  a  rivet  in  single  shear. 

PROBLEMS 

1.  Compute  the  shear  value  for  shop-driven  rivets  of  the  following  sizes: 
i,  If  f  >  s,  and  1  inch,  respectively,  for  (a)  single  shear  and  (b)  double  shear. 

2.  Compute  similar  values  for  field-driven  livets. 

Illustrative  Example.  In  the  case  illustrated  in  Fig.  61-a,  what 
thickness  of  plate  n  is  required  to  make  the  bearing  value  equal  the 
shearing  value?  The  shearing  value  is  5302  pounds.  The  bearing 

5302 
area  required  is  0.  nnn  or  0.212  sq.  in.    The   diameter  of   rivet 


being  0.75  in.,  tne  thickness  required  to  give  the  required  area  is 
0.212  sq.  in.  -5-  0.75  or  0.283  in.  The  next  higher  commercial  size 
is  0.3125  in.  or  ft  in.  thick. 

PROBLEMS 

1.  In  the  case  illustrated  in  Fig.  61-b  compute  the  thickness  of  plate  in 
required  to  make  the  bearing  value  equal  the  shearing  value. 

2.  Compute  the  thickness  of  plates  whose  bearing  values  correspond  to 
the  single  shear  values  of  Hn.,  |-in.,  g-in.,  and  1-in.  'rivets.    Compute  the  same 
for  double  shear  values. 


STEEL  CONSTRUCTION  67 

3.  How  many  J-in.  rivets,  field  driven,  single  shear  are  required  to  trans- 
mit 175,000  pounds? 

4.  How  many    1-in    rivets,  field  driven,  double  shear,  are  required   to 
transmit  100,000  pounds? 

5  Assume  shop  rivets  in  double  shear,  middle  plate  $-in  thick  How 
im»ny  f-in.  rivets  are  required  to  transmit  235,000  pounds?  How  thick  must 
be  the  outside  plates? 

The  designer  can  readily  fix  in  mind  the  thickness  of  plates 
which  give  bearing  values  corresponding  to  the  shear  values  of  the 
rivets,  then  it  will  be  necessary  to  compute  only  the  shearing  values. 

Friction.  If  the  plates  are  held  together  when  the  rivet  is 
driven,  the  shrinkage  in  length  as  the  rivet  cools  will  exert  consid- 
erable pressure  This  makes  the  riveted  joint  develop  a  frictional 
resistance,  which  is  additional  to  the  shear  and  the  bearing  resist- 
ance, The  amount  of  this  friction  has  not  been  accurately  deter- 
mined. Furthermore,  it  may  have  no  value  if  the  rivets  are  not 
tight.  Consequently,  no  account  is  taken  of  the  friction  in  figuring 
the  strength  of  riveted  joints 

Tension  Specifications  do  not  usually  assign  any  value  to 
rivets  in  tension.  While  their  use  in  this  manner  is  to  be  avoided, 
they  may  be  so  used  when  conditions  require  it  The  unit  stress 
allowable  is  the  same  as  for  shear  (See  p  51) 

Rivet  Tables.  The  handbooks  contain  tables  giving  the  shear- 
ing and  bearing  values  of  rivets  These  tables  cover  several  values 
of  unit  shearing  stress  and  unit  bearing  stress  They  give  the 
diameter  of  rivet,  area  of  cross  section,  single  shear,  double  shear, 
and  the  bearing  for  various  thicknesses  of  plates. 

PROBLEM 

Refer  to  tne  rivet  tables  and  check  all  the  examples  and  problems  that 
have  been  given. 

If  the  handbook  does  not  contain  tables  based  on  the  unit 
stresses  given  herein,  prepare  such  tables  and  keep  them  for  future 
use.  Most  handbooks  have  blank  pages  in  the  ^ack  part  of  the 
book  for  such  use.*  •*  f 

Investigation  of  Riveted  Joints.  The  theoretical  strength  of  a 
riveted  joint  involves  three  elements:  the  bearing  value  of  the 
rivets;  the  shearing  value  of  the  rivets;  and  the  area  of  the  section  of 
metal  after  deducting  rivet,  holes.- 

*The  student  should  become  familiar  with  all  the  tables  given  in  the  handbook  relating  to 
rivets  and  bolts. 


68 


STEEL  CONSTRUCTION 


In  a  perfect  design  these  three  elements  would  be  equal  in  value, 
but  this  ideal  is  rarely  reached.  Most  frequently  it  is  the  shearing 
value  which  determines  the  strength  of  the  joint,  next  the  bearing 
value,  and  least  frequently  the  section  of  the  metal. 

Illustrative  Example.  Fig.  62  illustrates  a  splice  of  two  plates, 
each  7"Xf".  Rivets  f"  diameter,  field  driven. 

(a)  Using  all  of  the  ten  rivets, 

Shear  value  10  X4418          =44,180# 

Bearing  value  10  X5625         =  56,250# 

Tension  value  at  (1)  '6|Xf  X  16,000  =  36,750 # 

Tension  value  at  (2)  5JXf  X  16,000  =  31, 500  # 

Loss  of  tension  value  between  (1)  and  (2)   =  5,250  # 

As  this  loss  is  more  than  the  amount  transmitted  from  m  to  n  by  the 


m      1 

1  »V 

iFf 

1 

/ 

z 

3 

4 

J 

e 

7 

Fig.  62.     Diagrammatic  Views  of  a  Riveted  Joint 

rivet  at  (1),  the  entire  tension  value  at  (1)  is  not  available  and  the 
strength  of  the  joint  is  the  tension  value  at  (2)  plus  the  shear  value 
of  the  rivet  at  (1),  or  31, 500+4418  =  35,918#. 

(b)  Now  consider  that  the  rivets  at  (1)  and  (7)  are  omitted. 

Shear  value  8 X4418         =  35,344# 

Bearing  value  8  X  5625          =  45,000  # 

Tension  value  at  (2)         5iXf  X  16,000  =  31, 500# 

The  strength  of  the  joint  is  the  tension  value  at  (2),  i.  e.,  31,500#. 

(c)  Next  consider  that  the  rivets  (4)  are  omitted. 
Shear  value  8  X  441 8  =  35,344  # 

Tension  value  at  (2)  plus  shear  value  of   rivet  at  (1)  as 
above  =  35,918  # 


STEEL  CONSTRUCTION  G9 

The  strength  of  the  joint  is  the  shear  value  35,344  #. 
<d)   Finally  omit  the  rivet  at  (3). 
Shear  value  9  X  4418  =  39,762  # 

Strength  of  joint  same  as  in  (a)   =  35,918  # 

From  the  above  it  is  clear  that  the  maximum  strength  of  the  joint 


? 


Fig.  63.     Diagrams  Showing  Right  and  Wrong  Arrangement  of  Rivet 
Holes  in  Tension  Members 

that  can  be  made  in  this  case  is  35,918  pounds.  It  requires  9  rivets 
as  in  (d).  Nearly  the  same  strength  can  be  secured  with  8  rivets  as 
in  (c),  35,344  pounds. 


Ni-n 


-i'rl 


i 
IH 

2 
3  2 

4 


a=Sum  of  gages  minus  thickness  of  angle 

\*  Rivets  can  be  taken  at  y%  less  than  for 
"  Rivets 


Note 


1"  Rivets  can  be  taken  at  y%  more  than  for 
Y*   Rivets 


Fig.  64.  Stagger  of  Rivets  Required  to  Maintain  Net  Section. 
From  "Standard*  for  Detailing"  American  Bridge  Company 


70 


STEEL  CONSTRUCTION 


The  important  point  to  be  observed  from  this  example  is  the 
difference  between  (a)  and  (b);  the  loss  of  section  by  rivet  holes 
should  be  made  as  gradual  as  possible. 

PROBLEM 

Go  through  the  operations  of  the  above  example  on  the  basis  of  shop  rivets. 

Net  Section.    The  holes  in  angles  can  usually  be  arranged  so 

that  only  one  need  be  deducted 
with  two  or  three  rows,  and  two 
with  four  rows.  This  is  not 
always  true  for  the  large  angles. 
Fig.  63  illustrates  the  right  and 
wrong  arrangement  of  holes  in  a 
number  o£  cases.  Fig.  64  illus- 
trates the  pitch  of  staggered 
rivets  required  to  maintain  the 
net  section.  If  the  joint  is  in 
compression  no  deduction  is  made  in  the  cross  section  on  account 
of  rivets,  and  the  rivets  need  not  be  staggered  unless  required  for 
minimum  spacing. 


GUSSCT   PLAJC. 


Fig.  65.     Two  Angles  Attached  to  a 
Gusset  Plate 


15  "I     42" 


2    L?   4  X  3  X 

\  6SOOO* 
Fig.  "66.     Side  and  End  View  of  a  Riveted  Hanger 

PROBLEMS 

1.    Fig.  65  shows  two  angles  in  tension  to  be  connected  to  a  gusset  plate 
with  shop  rivets.    Determine  the  following: 

Size  of  rivets 

Net  section  of  angles 


STEEL  CONSTRUCTION 


71 


Tension  value  of  net  section 

Thickness  of  gusset   plate  to  develop  the  full  double  shearing  value 
of  the  rivets 

Number  of  rivets 

Locate  gage  line  and  space  the  rivets 

Draw  plan,  elevation,  and  section  of  joint  at  J-inch  scale 
NOTE.    The  connection  illustrated  is  poor  on  account  of  secondary  stress, 
p.  234.     It  is  used  only  for  practice. 

2.    Fig.  66  shows  a  hanger  connected  to  the  underside  of  an  I-beam. 

The  hanger  is  made  of  2  Ls  4*X3'X|*  and  carries  a  load  of  65,000 
pounds.    Determine  the  following! 

Size  of  rivets 

Total  section  of  two  angles 

Net  section  of  two  angles  after  deducting  one  rivet  hole  from  each 

Whether  section  is  sufficient  for  the  load  applied 

Thickness  of  gusset  plate  to  develop  the  double  shearing  value  of  rivets 

Number  of  shop  rivets  to  connect  lug  angles  to  main  angles    (assume 


S"  I     42* 


Fig    67      Side  and  End  View  of  Standard  Beam  Connection 

that  one-half  of  load  is  transmitted  through  the  lug  angles) 

Number  of  shop  rivets  to  connect  hanger  to  gusset  plate 
Number  of  shop  rivets  to  connect  gusset  plate  to  top  angles 
Number  of  field  rivets  (in  tension)  to  connect  top  angles  to  I-beam 
Make  drawing  at  f-inch  scale,  showing  all  dimensions  and  rivet  spacing 
Give  page  numbers  of  handbook  for  ah1  references  used  In  the  above  opera- 
tions 

3  Fig.  67  shows  the  standard  end  connection  for  a  15'  I  42#.  What 
is.  the  strength  of  the  connection? 

Bolts.*  The  foregoing  discussion  of  rivets  applies  also  to  bolts, 
except  as  to  stresses  allowed  and  as  to  bolts  in  tension. 

Turned  bolts  fitting  tight  in  reamed  holes  have  the  same  values 
as  fieJd  rivets.  Machine  bolts  should  be  allowed  only  three-fourths 
the  unit  stresses  of  field  rivets,  i.  e.,  7500  pounds  per  square  inch 
shear  and  15,000  pounds  per  square  inch  bearing. 


*The  student  should  obtain  a  catalogue  from  a  bolt  manufacturer  and  become  familiar 
with  the  standard  and  special  bolts  on  the  market. 


72 


STEEL  CONSTRUCTION 


In  general,  the  use  of  bolts  in  the  permanent  structure  should 
be  discouraged,  being  limited  to  locations  where  it  is  impracticable 
to  drive  rivets  and  to  connections  where  they  serve  simply  to  hold 
the  members  in  position  and  do  not  transmit  stress.  The  cost  of 
using  turned  bolts  will  prevent  their  use  where  rivets  can  be  used. 
But  machine  bolts  are  cheaper  than  rivets  for  most  field  connections 
and  their  use  must  be  forbidden  except  in  cases  where  they  are 
suitable. .. 

Turned  Bolts.  Turned  bolts,  as  the  name  indicates,  are  turned 
to  exact  diameter  in  a  lathe.  The  holes  <  for  turned  bolts  must  be 
Teamed  after  the  members  are  assembled,  or  both  members  must 

be  reamed  to  fit  the  same  tem- 
plate. The  reamer  must  have 
the  same  diameter  as  the  finished 
bolt  so  as  to  give  a  driving  fit. 

Washers  must  be  used  under 
both  the  head  and  nut.  Refer 
to  Fig.  ^68  and  note  that  there  is 
a  fillet  under  the  head.  If  the 
washer  is  not  used,  this  fillet  will 
prevent  the  head  from  bearing 
against  the  plate.  If  the  thread 
is  cut  long  enough  to  allow  the 
nut  to  bear  against  the  plate,  the 
thread  will  extend  into  the  hole; 
hence  a  washer  is  used  so  that 

the  thread  need  not  be  cut  so  long.  After  the  nut  is  drawn  up 
tight,  the  threads  should  be  checked  with  a  chisel  so  that  it  cannot 
become  loosened. 

Machine  Bolts.  Machine  bolts  are  made  from  rods  as  they 
come  from  the  rolling  mill  and  are  not  finished  to  exact  size.  They 
do  not  fill  the  holes  fully.  Their  principal  use  is  for  assembling 
material  in  the  shop  or  in  the  structure,  preparatory  to  riveting. 
They  may  remain  in  the  finished  structure  if  not  subjected  to  shear. 
Such  a  case  is  a  beam  resting  on  another. 

Bolts  in  Tension.  When  a  bolt  is  used  in  tension,  the  net  area 
available  to  resist  the  stress  is  the  area  at  the  root  of  the  thread. 
For  example,  determine  the  tensile  strength  of  a  f-inch  bolt.  Re- 


Fig.  68.    Part  Section  of  Bolted  Joint 
Showing  Fillet  Under  Bolt  Head 


STEEL  CONSTRUCTION  73 

ferring  to  the  handbook,  it  is  found  that  the  diameter  at  the  root  of 
the  thread  is  0.62  inches.  From  this,  the  area,  if  not  given  in  the 
table,  can  be  computed  and  is  found  to  be  0.30  square  inch.  Then 
the  tension  value  is  0.30X10,000  or  3000  pounds. 

Two  nuts  should  be  used  on  bolts  in  tension  to  prevent  strip- 
ping the  threads,  and  the  threads  should  be  checked  after  the  nuts 
are  tightened. 

Length  of  Rivets  and  Bolts.  The  grip  of  a  rivet  or  bolt  is  the 
thickness  of  the  material  through  which  it  passes.  The  grip  esti- 
mated is  the  nominal  thickness  of  metal  plus  Jg  inch  for  each  piece 
of  metal. 

The  length  of  rivet  required  for  a  given  case  is  the  grip  plus  the 
amount  of  stock  required  to  form  the  head  and  for  filling  the  hole 
when  the  rivet  is  upset.  The  lengths  required  for  various  grips  are 
given  in  the  handbooks. 

The  length  of  bolt  required  for  a  given  case  is  the  grip  plus  the 
thickness  of  the  washers,  plus  the  thickness  of  the  nut  (or  two  nuts 
if  in  tension),  plus  \  inch. 


CRANE  COMPANY  OFFICE  BUILDING,  CHICAGO 
Holabird  &  Roche,  Architects 


CONSTRUCTION 

PART  II 


BEAMS 

Definitions.  A  beam  is  a  structural  member  subjected  to  a  load 
applied  perpendicular  to  its  longitudinal  axis.  Usually  the  beam  is 
in  a  horizontal  position  and  the  load  is  applied  vertically  downward. 
It  is  supported  at  the  ends  (unless  it  is  a  cantilever).  The  space 
between  the  supports  is  the  span. 

The  word  beam  is  a  general  term  which  applies  in  all  cases  to 
a  member  subjected  to  bending  by  a  transverse  load,  irrespective  of 
the  use  to  which  it  is  put.  There  are  a  number  of  special  terms 
which  have  reference  to  the  position  or  use  of  the  beam. 

A  joist  is  a  beam  which  supports  the  floor  or  other  load  direct. 

A  girder  is  a  beam  which  supports  one  or  more  joists  or  other 
beams. 

A  lintel  is  a  beam  which  supports  the  wall  above  an,  opening 
therein. 

A  spandrel  beam  is  one  which  supports  the  masonry  spandrel 
between  the  piers  of  a  wall. 

Elsvator  beams,  sheave  beams,  stair  stringers,  crane  girders, 
etc.,  are  used  for  the  purposes  indicated  by  their  names. 

Built-up  beams  are  usually  called  "girders"  irrespective  of  their 
uses.  There  are  plate  girders,  box  girders,  beam  box  girders,  etc. 

The  span  of  a  beam  is  the  distance  between  supports,  or,  in  the 
case  of  a  cantilever,  the  distance  from  the  support  to  the  end  of  the 
beam. 

Classification.  Beams  are  classified  as  simple  and  restrained. 
A  simple  beam  is  one  which  has  a  single  span  and  merely  rests  on  its 
supports,  there  being  no  rigid  connection  to  prevent  normal  bending. 
A  restrained  beam  is  one  which  has  more  than  one  span  or  is  rigidly 
connected  at  one  or  more  supports,  or  otherwise  prevented  from 
normal  bending.  Fig.  G9  illustrates  a  simple  beam  and  several 


76  STEEL  CONSTRUCTION 

forms  of  restrained  beams,  showing  in  an  exaggerated  way  the  forms 
they  assume  when  bending  under  load. 

Although  most  beams  in  steel  construction  are  somewhat 
restrained  by  their  end  connections,  they  are  treated  as  simple 
beams  in  designing.  Beams  extending  over  more  than  two  supports 
are  very  rarely  used  in  building  construction  and  are  not  considered 
in  this  text.  Cantilever  beams  occur  in  the  form  of  a  beam  pro- 
jecting from  a  support  to  which  it  is  rigidly  attached,  and  in  the 
form  of  a  beam  spanning  from  one  support  to  another,  and  pro- 
jecting beyond  one  or  both  supports. 

Sections.  The  structural  steel  section  most  used  as  a  beam  is 
the  I-beam.  It  is  designed  for  this  purpose  and  is  the  most  efficient 
form  in  which  the  steel  can  be  made  for  resisting  bending.  Chan- 
nels, angles,  and  tees  are  used  only  to  meet  some  special  condition. 
The  built-up  or  riveted  girders  imitate  the  I-beam  and  are  used  for 


A  T~^  A 

Fig.  69.     Simple,  Cantilever,  and  Restrained  Beams 

loads  which  are  too  great  to  be  supported  by  the  rolled  section. 
This  part  of  the  text  deals  only  with  rolled  sections.  Riveted  sec- 
tions are  given  later, 

REVIEW  OF  THEORY  OF  BEAM  DESIGN 

Factors  Required  in  a  Complete  Design.  The  complete  design 
of  a  beam  requires  the  computation  of  the  bending  moments  and 
shears  resulting  from  the  assumed  loading,  and  of  the  resisting 
moment,  shearing  resistance,  and  deflection  of  the  beam  section 
which  it  is  proposed  to  use.  The  resisting  moment  usually  governs. 

Maximum  Bending  Moment.  The  resisting  moment  based  on 
the  allowable  unit  stress  must  be  equal  to  or  greater  than  the  maxi- 
mum bending  moment.  As  the  section  of  the  rolled  beam  is  the 
same  from  end  to  end,  its  resistance  is  constant  throughout  its 


STEEL  CONSTRUCTION  77 

length.  Hence,  it  is  necessary  to  compute  only  the  maximum 
bending  moment.  The  position  and  amount  of  the  maximum 
bending  moment  are  computed  later  in  the  text  for  various  conditions 
of  loading. 

Maximum  Shear.  The  shearing  resistance  based  on  the  allow- 
able unit  stress  must  be  equal  to  or  greater  than  the  maximum 
shear.  The  shearing  resistance  of  the  rolled  beam  is  constant 
throughout  its  length.  Hence,  it  is  necessary  to  compute  only  the 
maximum  shear.  The  position  of  maximum  shear  in  single  span 
beams  is  always  adjacent  to  the  support  which  has  the  greater 
reaction. 

Deflection.  A  beam  subjected  to  bending  stresses  must  have 
some  deflection,  and,  under  certain  conditions,  the  amount  of  this 
deflection  must  be  limited.  For  example,  the  floor  section,  Fig.  70, 
shows  that  the  deflections  in  the  joists  were  so  great  as  to  cause  a 
bad  crack  hi  the  marble  floor  above  the  steel  girder. 


•  '•'*•'''.  '  :.*v  I'1'*-  V;-V  ••;'•:  ^ivY.-A.'s'' 

c.  ;..tj     fnm       g  ..  ^  .'...''  
^^:';v'.^'!':::<r;v:/^^V;/-*;-'v.\;':  ;  \ 

£-  CONCRETE   flLL 
JOIST 

MI 

GIRDER 

mm 

Fig.  70.     Floor  Section  Showing  Crack  Over  Girder,  Due  to  Deflection  of  Joists 

The  definitions  and  methods  of  computing  bending  moments, 
shears,  resisting  moments,  shearing  resistance,  and  deflection  are 
given  in  "Strength  of  Materials/'  The  student  should  review 
those  topics  before  proceeding  with  this  text.  The  following  brief 
discussion  may  help  to  fix  in  mind  the  important  points. 

Flexure.  It  is  a  matter  of  common  observation  that  a  loaded 
beam  deflects  or  sags  between  the  supports.  This  is  most  evident  in 
wood  beams,  but  is  true  of  beams  of  all  materials.  This  deflection 
stretches  the  fibers  at  the  bottom  of  the  beam,  i.  e.,  produces  tension; 
and  shortens  the  fibers  at  the  top  of  the  beam,  i.  e.,  produces  com- 
pression. Somewhere  between  the  top  and  the  bottom  the  fibers 
are  neither  stretched  nor  shortened,  hence  there  is  no  stress;  this 
place  is  called  the  "neutral  axis"  and  passes  through  the  center  of 
gravity.  In  I-beams  and  channels  the  neutral  axis  is  at  mid-depth. 


78  STEEL  CONSTRUCTION 

This  is  also  true  of  rectangular  wood  beams.  The  intensity  of 
stress— tension  or  compression — corresponds  to  the  amount  of  defor- 
mation— lengthening  or  shortening;  hence,  the  intensity  varies  with 
distance  from  the  neutral  axis,  being  zero  at  the  neutral  axis  and 
maximum  at  the  extreme  fibers*  at  the  top  and  bottom.  This  is 
illustrated  in  Fig.  71.  The  stress  on  the  extreme  fiber — not  the 
average  stress — governs  in  designing.  The  working  or  unit  stress 
allowed  is  16,000  pounds  per  square  inch  in  both  the  tension  and  the 
compression  flanges.  (See  Unit  Stresses,  p.  51.) 

In  Fig.  71  assume  that  each  arrow  represents  the  stress  on  a  unit 
area,  the  length  of  the  arrow  representing  amount  or  intensity  of  the 
stress.  To  find  the  resistance  of  the  beam  to  bending  it  must  be 
remembered  that  the  resisting  moment  is  the  sum  of  the  moments 

-    of  all  stresses  about  the  neutral 
7c oppression   axis.     Under  Strength  of  Beams, 
in  "Strength  of  Materials/'  Part 
I,  it  is  shown  that  the  resisting  mo- 
ment is  expressed  by  the  formula 


NEUTRAL    AXIS 


Fig.  71.     Graphical  Representation  of  Stresses  in  •»*       o   / 

the  Fibers  of  a  Beam  M  =  - 

C 

in  which  M  is  resisting  moment  in  inch-pounds;  /  is  the  moment  of 
inertia  in  terms  of  inches;  c  is  the  distance  from  the  neutral  axis  to 
the  extreme  fiber  in  inches;  and  S  is  the  maximum  fiber  stress,  that 
is,  the  stress  on  the  extreme  fiber  in  pounds  per  square  inch.  From 
this  formula  the  resisting  moment  of  the  beam  can  be  computed. 

Assume  a  12"  I  31  J#.  From  the  handbook  the  value  of  /  is 
215.8.  The  distance  from  the  neutral  axis  to  the  extreme  fiber  is 
6  inches.  The  allowable  unit  stress  on  the  extreme  fiber  is  16,000 
pounds  per  square  inch.  Then 

„     S  I     16,000X215.8     ._,  _.  .     „ 
M  =  —  =  —  —  =  575,467  in.-lb. 

c  6 

When  the  unit  stress  S,  resulting  from  a  given  bending  moment, 
is  required,  the  formula  is  transposed  into  the  form 

J/c 


*The  term  extreme  fiber  is  correctly  used  in  relation  to  wooden  beams  as  wood  is  a  fibrous 
material.  Steel  is  not  a  fibrous  material  but  the  term  expresses  the  idea  clearly  and  is  generally 
used. 


STEEL  CONSTRUCTION  79 

Assume  that  the  bending  moment  is  500,000  inch-pounds  and  that 
the  beam  is  12"  I  3li#,  then, 

„    500,000  X6_1Qnm^' 

215.8 

Vertical  Shear.  Fig.  72  illustrates  a  beam  with  a  heavy  load 
applied  close  to  one  support.  There  is  a  tendency  for  the  part  on 
the  left  of  the  vertical  plane  a  a  to  slide  downward  in  relation  to  the 
part  on  the  right,  This  is  prevented  by  the  shearing  resistance  of 
the  beam.  This  shearing  tendency  exists  throughout  the*  length 
of  the  beam  but  is  greatest  near  the  supports.  In  this  case  the 
maximum  shear  is  adjacent  to  the  right  support  at  a  a  and  is 
assumed  to  be  45,000  pounds.  It  is  resisted  by  the  strength  of  the 
steel  at  this  section.  The  average  stress  over  this  section  is  the 
total  vertical  shear  divided  by  the  area  and  is  expressed  by  the  formula 

o        V  _  l,a 

' 


in    which    S8     equals    shearing 

,  Fig.  72.     Diagram  Illustrating  Shear  on  a  Beam 

stress  per  square  inch;  V  equals 

total  vertical  shear;  and  A  equals  area  in  square  inches. 
But  it  can  be  shown  that  the  shear  is  not  uniform  over  this  area, 
being  zero  at  the  extreme  fiber  and  a  maximum  at  the  neutral  axis. 
The  exact  maximum  value  is  difficult  to  compute,  but  it  can  be 
determined  approximately  by  assuming  that  the  entire  shear  is 
resisted  by  the  web  of  the  beam  (see  Resisting  Shear,  "Strength  of 
Materials"  Part  II)  ;  then  the  above  formula  is  used,  making  A  equal 
the  area  of  the  web  in  square  inches.  In  this  case  assume  that  the 
beam  is  12"  I  31  J#.  The  area  of  the  web  is  approximately  12"  X 


.35"  =  4.9  sq.  in.    Then  S.  =  or  10,714  pounds  per  square 

inch.    The  allowable  value  given  under  Unit  Stresses  is  10,000 
pounds  per  square  inch,  and  the  beam  is  over-stressed  in  shear. 

If  it  is  desired  to  compute  the  maximum  resistance  to  shear  for 
this  beam,  the  formula  is  put  in  the  form 

V  =  S8XA 
and  for  this  case 

F=  10,000X4.2  =  42,000# 
A  beam  subjected  to  an  excessive  load  would  not  fail  by  the 


80  STEEL  CONSTRUCTION 

actual  shearing  of  the  metal  along  the  plane  a  a  but  by  the  buckling 
of  the  web.  This  has  been  taken  into  account  in  establishing,  the 
unit  stress. 

Deflection.    As  previously  stated,  a  beam  which  is  subjected 
to  bending  stresses  must  deflect  a  certain  amount.    The  amount  of 
deflection  depends  on  the  load,  the  length  of  span,  and  the  section 
of  the  beam.     It  is  expressed  by  the  formulas: 
(1)  For  a  uniformly  distributed  load 


384   El 
(2)  For  a  load  concentrated  at  center  of  span 

1  Wl* 
d=^~EI 

in  which  d  equals  deflection  in  inches;  W  equals  total  load  in  pounds; 
I  equals  span  in  inches;  /  equals  moment  of  inertia;  and  E  equals 
modulus  of  elasticity  equals  30,000,000. 

Modulus  of  Elasticity.  The  modulus  of  elasticity  is  the  ratio  of 
the  unit  stress  to  the  unit  deformation.  If  a  piece  of  steel  one  inch 
-square  and  ten  inches  long  is  subjected  to  a  tensile  stress  of  20,000 
pounds,  the  unit  stress  is  20,000  pounds  per  square  inch.  The  steel 

is  elongated  about  —  :  inch  and,  therefore,  the  unit  deformation,  or 
lou 

the  elongation  of  one  inch  in  length,  is  —  -  inch.    Then  the  ratio  of 

1500 

20  000 
unit  stress  to  unit  deformation  is  —  -  —  =  30,000,000.    This  ratio 

1500 

has  been  determined  by  experiment.  It  is  the  same  for  both  tension 
and  compression.  Other  materials  have  other  values. 

CALCULATION  OF  LOAD  EFFECTS 

Uniformly  Distributed  Loads.  The  first  step  in  designing  a 
beam  is  to  determine  the  bending  moments  and  shears  resulting 
from  the  assumed  loading.  The  methods  of  computing  them  are 
given  under  External  Shear  and  Bending  Moment,  "Strength  of 
Materials,"  Part  I. 


STEEL  CONSTRUCTION 


81 


Joists.  The  loads  on  joists  are  usually  distributed  uniformly 
along  the  length  of  the  beam.  Assume  that  the  simple  beam,  Fig. 
73,  has  a  span  L=17'-6",  and  supports  a  load  of  800  pounds  per 
lineal  foot. 

Total  load  =H'=  17.5X800 

=  14,000  # 

Since  the  load  is  uniformly  distri- 
buted, the  reactions  are  equal: 

Fig.  73.     Diagram  of  Beam  Uniformly  Loaded 


The  maximum  shear  occurs  adjacent  to  each  support  and  its 
amount  is  the  same  as  the  reaction,  hence  V  ^  and  \\  have  the  same 
values  as  Rl  and  R2. 

The  maximum  bending  moment  occurs  at  the  middle  of  the 
span  and  has  a  value 


=  7000X8.  75  =61,250ft.-lb. 


iwx 


17.5 


>  7000  X  4. 375  =  30,625  ft.-lb. 


M  =  30,625  ft.-lb.  =  367,500  in.-lb. 

The  formula  for  this  bending  moment  is 

M  =  J  W  L  =  lX  14,000X17.5  =  30,625  ft.-lb. 

Cantilever  Beam.     Fig.  74. represents  a  cantilever  beam  support- 
ing a  uniformly  distributed  load.   Assume 
the  length  L  of  cantilever  to  be  8'-9", 
and  the  load,  800  pounds  per  lineal  foot; 
then 

PF  =  8. 75X800  =  7000$ 


The  maximum  bending   moment    is  at      Fig.  74.   Diagram  of  Cantilever 

Uniformly  Loaded 

the  support,  and  therefore 

M  =  W  X  ^ = 7000  X  4 . 375  =  30,625  ft.-lb. 
Compare  these  results  with  those  obtained  for  the  simple  span 


82 


STEEL  CONSTRUCTION 


having  the  same  load  per  lineal  foot.    The  span  is  one-half  as  much, 
while  the  shear  and  the  bending  moment  are  the  same. 

Combination  Simple  and  Cantilever  Beam.  A  beam  resting  on 
two  supports,  projecting  beyond  one  of  them,  and  supporting  a  uni- 
formly distributed  load  is  represented  in  Fig.  75.  Assume  the 
span  L  between  supports  to  be  17'-6",  the  length  L'  of  the  canti- 
lever to  be  8'-9",  and  the  load  800  pounds  per  lineal  foot;  then 
TT=(800X17.5)  +  (800X8.75)=21,000# 

The  reactions  must  be  determined  by  the  method  of  moments. 
Take  the  moments  about  Rv.  For  the  positive  moment  the  lever 
arm  is  the  distance  from  Rl  to  the  center  of  gravity  of  the  entire 
beam,  viz,  13.125  feet;  therefore 

Positive  moment  =  21,OOOX!3.125  =  275,625  ft.-lb. 


Fig.  75.     An  Overhanging  Beam  with  Shear  and  Moment  Diagrams 


The  negative  moment  must  equal  the  positive  moment;  then 

R2XL  =  275,625 

and  the  value  of  R2  is  found  by  dividing  the  positive  moment  by  the 
distance  L  between  supports.' 

275,625 
Therefore  R2=  = 


STEEL  CONSTRUCTION  83 

Now  since  the  sum  of  the  reactions  must  equal  the  total  load,  the 
value  of  R<  can  be  determined  by  subtracting  R2  from  W;  then 

R,  =  21,000-  15,750  =  5250# 
This  value  of  Rt  can-  be  checked  by  taking  moments  about  R2. 

The  position  of  the  maximum  shear  is  not  self-evident  so  the 
shear  values  must  be  computed.  Ft  =5250.  Proceeding  toward  the 
right,  800  pounds  is  deducted  for  each  foot,  so  the  shear  becomes 
zero  at  6.5625  feet  from  Rlf*  continuing  to  a  point  just  to  the  left 
of  7?a,  the  value  of  the  shear  is 

F2=5250-(800X17.5)  =  -8750# 

Continuing,  to  the  right,  add  the  value  of  R2,  then  the  value  of  the 
shear  is 

F3=  -8750+15,750  =  +7000  # 

Continuing,  the  shear  reduces  at  the  rate  of  800  pounds  per  lineal 
foot,  becoming  zero  at  the  end  of  the  cantilever.  The  above  values 
are  shown  graphically  on  the  shear  diagram. 

The  maximum  positive  bending  moment  is  between  /?,  and  R2 
at  the  same  position  as  the  zero  shear.  Its  value  is 

f-f  5250X6.5625  »  4-34,448) 

U  +17,224  ft.-lb. 

1-800X6.  5625X^~^«  -17,224  J 


The  maximum  negative  bending  moment  is  at  Rv    Its  value 
computed  on  the  right  is 

-800X8.  75X^p=  -30,625  ft.-lb. 

or  computed  on  the  left  is 

f  +5250X17.  5  =+  91,875) 

I  =  -30,625  ft.-lb. 

U  800X17.  5X^=  -122,500  J 

The  moment  diagram  can  be  constructed  by  computing  the  values 
at  points  one  foot  apart  and  plotting  the  results.  From  this  dia- 
gram it  will  be  noted  that  the  bending  moment  changes  from  positive 
to  negative  at  the  point  x.  This  is  called  the  "point  of  contra- 
flexure"  and  in  this  case  it  is  located  13.125  feet  from  Rt. 


84  STEEL  CONSTRUCTION 

It  is  usually  easier  to  compute  the  bending  moment  for  simple 
spans  uniformly  loaded  from  the  formula 


and  for  cantilevers  from  the  formula 


For  the  combination  span  illustrated  above,  the  maximum  negative 
moment  may  be  computed  from  the  cantilever  formula.  But  the 
maximum  positive  moment  cannot  be  expressed  in  a  simple  formula 
and  must  be  computed  by  means  of  the  summation  of  moments  as 
illustrated. 

EXAMPLES  FOR  PRACTICE 

1.     A  joist  has  a  span  of  21  feet.     It  supports  a  floor  area 
5|  feet  wide.    The  floor  construction  weighs  115  pounds  per  square 


— 5-O  f- —  15 -O    —  '   »H» — 4-O  — 

Fig.  76.     Uniformly  Loaded  Beam  Overhanging  at  Both  Ends. 


foot  and  the  live  load  to  be  supported  is  50  pounds  per  square  foot. 
Compute  the  shear  and  bending  moment. 

2.  What  are  the  maximum  shear  and  bending  moment  for  a 
total  load  of  80,000  pounds  uniformly  distributed  on  a  span  of  8 
feet;  10  feet;  12  feet;  14  feet;  16  feet?    What  is  the  ratio  of  the 
bending  moments  for  the  8-foot,  and  the  16-foot  spans? 

3.  Compute  the  maximum  shears  and  bending  moments  for  a 
beam  supporting  a  uniformly  distributed  load  of  1,000  pounds  per 
lineal  foot  on  a  span  of  8  feet;  10  feet;  12  feet;  14  feet;  16  feet.     What 
is  the  ratio  of  the  bending  moments  for  the  8-foot  and  16-foot  spans? 

4.  Compute  the  maximum  shears  and  bending  moments  for 
cantilevers  from  the  data  given  for  the  preceding  problem.     Com- 
pare the  results  with  those  for  the  simple  beam. 

5.  Fig.  76  represents  a  beam  extending  beyond  both  supports. 
Its  load   is  600  pounds  per  lineal  foot.     What  is  the  maximum 
shear?  ^  What  are  the  bending  moments  at  7?,  and  7?2?     What  is 
the  maximum  positive  bending  moment? 


STEEL  CONSTRUCTION  ,  85 

6.  Construct  the  shear  and  moment  diagrams  for  the  preced- 
ing problems. 

7.  Given  a  span  of  20  feet  and  a  bending  moment  of  50,000 
foot-pounds,  what  is  the  total  uniformly  distributed  load? 

50,000X8 


20 

8.    Given  a  span  of  18  feet  and  a  bending  moment  of  72,000 
foot-pounds,  what  is  the  load  per  lineal  foot? 

Concentrated    Loads.    Girders   in   floor   construction   usually 
receive    their    loads    at    points 
where  joists  connect.  P          I*          f*         '  P 

Simple  Beam.    Fig.  77  rep-    j~j-<?^[~-  «-o=-[>-  4-0'-^  ^o'^z-o^ 
resents  a  simple  beam  supporting  C 
the  concentrated  loads  Pv  P5,  P3, 
and  P4.     The  loads  are 

Pt=  60,000  # 
P2=  80,000  # 
P3=  80,000  # 

•^4  =    50>QQQflr  Fig.  77.     Simple  Beam  with  Concentrated  Loads. 

Total  load  =  270,000  # 

To  determine  the  reaction  R2,  take  moments  about  Rt : 

3X60,000  =  180,000 

7X80,000  =  560,000 

11X80,000  =  880,000 

15X50,000  =  750,000 

2,370,000  ft.-lb. 


2 

Similarly,  to  determine  the  reaction  Rlt  take  moments  about  R2: 

2X50,000  =  100,000 

6X80,000  =  480,000 

10X80,000  =  800,000 

14X60,000  =  840,000 

2,220,000  ft.-lb. 


Therefore  Rt+R2  =  130,588+1  39,412  =  270,OCO# 

which  checks  with  the  total  load. 


86  STEEL  CONSTRUCTION 

The  maximum  shear  occurs  at  the  left  of  #2  and  is  139,412 
pounds.  By  constructing  the  shear  diagram,  it  is  found  that  the 
shear  passes  from  positive  to  negative  at  P2.  This  position  of  zero 
shear  establishes  the  point  of  maximum 
moment.  Computing  the  moment  from 
the  loads  and  reaction  on  the  left 
gives 

i  +7X130,588  = +914,116 
-4X  60,000  =-240,000 

Fig.  78.     Cantilever  Beam  with 

^ncentrated  Loads  +674,116  ft.-lb. 

Computing  on  the  right  gives 

+  10X139,412=  +1,394,120 

-  4X  80,000  =  320,000 

-  8X  50,000  =  400,000        -    720,000 

+    674,120  ft.-lb. 

Cantilever  Beam.  Fig.  78  represents  a  cantilever  supporting 
the  concentrated  loads  P1  and  P2. 

R  =  P, + P2  =  30,000+40,000 = 70,000  # 

The  maximum  shear  is  70,000  at  the  right  of  R.    Zero  shear  is  at 
the  right  of  P2.    ' 
The  maximum  bending  moment  is  at  R.    It  is 

-4X30,000  =-120,000 
-9X40,000= -360,000 

-"480^000  ft.-lK 

Simple  Beams  on  Two  Supports  and  Projecting  at  Both  Ends. 
Fig.  79  represents  a  beam  resting  on  two  supports  and  projecting 
beyond  both  of  them.  Jt  supports  concentrated  loads  as  shown. 
The  loads  are 

Pt  =  15,000# 

P2=  15,000  # 

P8=  15,000# 

P4=  15,000  # 

P6=  15,000# 

P«=  30,OOQ# 

Total  load  - 105,000  # 


STEEL  CONSTRUCTION 


To  determine  the  reaction  R2,  take  moments  about  Rt: 

0X15,000  (P2)  =  00,000 

4X15,000  (P8)  =  60,000 

8X15,000  (P4)  =120,000 

12X15,000  (P6)  =180,000 

16X30,000  (Ptt)  =480,000       840,000  ft.-lb. 

-  4X15,000  (Pt)  =  "    -  60,000 

Moment  of  reaction  /?,=  780,000  ft.-lb. 

y  *t  &  *t  \  *k 

L — 4\L,  _»L — j.0'- — 4- — t'-o"    4" — </-<?' —4- — ^  o — H 


Fig.  79.     Overhanging  Beam  with  Concentrated  Loads      Shear 
and  Moment  Diagrams 


To  determine  the  reaction  Rlt  take  moments  about  R2: 
OX  15,000  (P5)=  00,000 
4X  15,000  (P4)=  60,000 
8  X  15,000  (P8)  =  120,000 
12X  15,000  (P2)  =  180,000 
16-X  15,000  (PJ  =  240,000       600,000  ft.-lb. 
-  4X30,000  (P,)=  "    -120,000 

Moment  of  reactionflt  =  480,000  ft.-lb. 


88  STEEL  CONSTRUCTION 

Therefore 


i 

The  shear  values  are 

F,  =  15,000 
F2=--  10,000 
Fs  =  20,000 
F4  =  30,000 
Zero  shear  occurs  at  P3. 

The  bending  moments  are  maximum  negative  at  7?j  and  R2  and 
maximum  positive  at  Ps.  Their  values  are 

at^   M=   -4X15,000=  -  60,000  ft.-lb. 

at/?2  M=   -4X30,000=  -  120,000  ft.-lb. 

[+4X40,000  =  +  160,000 
atPs  M  =  \  -4X15,000=-  60,000 

1-8X1  5,000  =  -  120,000  -  20,000  ft.-lb. 

From  the  last  result,  it  develops  that  the  bending  moment  at  P3  is 
minimum  negative  (not  considering  the  ends  of  the  cantilevers)  and 
not  maximum  positive.  Hence  there  is  no  reversal  of  moment  in 
this  case.  The  moment  diagram  shows  this. 

EXAMPLES  FOR  PRACTICE 

1.  Solve  the  preceding  case  for  the  following  loads:  Pt  = 
10,000#;  P2  =  10,000#;  P3  =  1  5,000  #;  P4  =  20,000  #;  P6  =  20,000#; 
P6  =  l  5,000  #.    Construct  the  shear  and  moment  diagrams. 

2.  What  are  the  maximum  shear  and  bending  moment  for  a  load 
of  40,000  pounds  at  the  center  of  an  8-foot  span?    Of  a  10-foot 
span?    Of  a  12-foot  span?    Of  a  14-foot  span?    Of  a  16-foot  span? 
What  is  the  ratio  of  the  bending  moments  for  the  8-foot  and  16-foot 
spans? 

Compare  these  results  with  those  from  the  second  problem 
under  uniformly  distributed  loads  and  note  that  the  bending  moments 
are  the  same  though  the  uniformly  distributed  load  is  twice  the 
concentrated  load. 

3.  Compute  the  shear  and  bending  moment  for  two  loads  of 
40,000  pounds  each,  placed  at  the  third  points  of  a  16-foot  span;  at 
the  quarter  points.    Compare  with  the  preceding  problem. 


STEEL  CONSTRUCTION 


89 


4.  A  load  at  the  center  of  a  20-foot  span  produces  a  bending 
moment  of  200,000  foot-pounds.    What  is  the  load? 

5.  Two  equal  loads  at  the 

quarter  points  of  a  20-foot  span  ^      ,    ,^ 

produce  a   bending  moment  of 
100,000  foot-pounds.    What  are  [ 


I  f\oAs  TTr.rl*»i.  Fig.  80.     Simple  Beam  with  Uniformly  Distribu- 

LUdUS.          UIH  ted  Load  over  Part  of  Span 


the  loads? 
Combined 

"combined  loads"  are  considered 
the  combinations  of  uniformly  distributed  and  concentrated  loads,  and 
of  uniformly  distributed  loads  on  parts  of  spans.  In  computing 
moments  in  these  cases,  the  uniformly  distributed  load  may  be  con- 
sidered as  concentrated  at  its  center  of  gravity,  Fig.  80,  unless  the 
center  of  moments  is  within  the 
space  occupied  by  the  load;  in 
which  case  the  parts  of  the  load 
to  the  right  and  to  the  left  of  the 
center  of  moments  must  be  con- 


K 


Simple  Beam  with  Variable  Load 


sidered  as  concentrated  at  their 
respective  centers  of  gravity. 
Thus,  if  the  center  of  moments 

is  at  Rl  or  R2,  the  concentrated  load  P  is  used;  but  if  the  center 
of  moments  is  at  0  the  concentrated  loads  P,  and   P2  are  used. 
The  same  principle  applies  if  the  distributed  load  is  variable  instead 
of  uniformly  distributed,  Fig.  81. 
Full  Length  Distributed  Load 
and  Concentrated  Load.     Fig.  82 
illustrates   a  beam  with  a  uni- 
formly    distributed     load     full 
length  and  a  concentrated  load, 
as  shown. 

Total  load  =  1 0,000 #  (u.d.) 

+  10,000#  (con.)  =  20,000# 
Moments  about  Rl  are 
10X10,000=100,000 
15X10,000  =  150,000 

Fi«.  82.  _Simple  Beam  with  Uniformly  Distribu- 
id  over  Entire  Length  and  One 
Concentrated  Load 


^D.  =  5cc*.p[.fi ' j.  //vh 


•  10000  * 
[—  5-0"- 


STEEL  CONSTRUCTION 


Therefore 


250,000 


- 12,500  # 
7500  # 


20 

/?!  =  20,000 -12,500  = 
Maximum  shear  is  12,500  #.     Zero  shear  occurs   under  the 
load  P.    Hence  this  is  the  point  of  maximum  bending  moment. 
The  bending  moment  computed  on  the  right  is 
+5  XI 2,500  =+62,500 

-  2^X5X500=  -  6,250 

56,250  ft.-lb. 

The  bending  moment  computed  on  the  left  is 
+  15  X  7,500    =  +  112,500 

-  7JX 15X500=-  56,250 

56,250  ft.-lb. 


SMC  A  ft  DIA  6RA  M 


Fig.  83.     Simple  Beam  with  Two  Rates  of  Uniformly  Distributed  Load 


Two  Uniformly  Distributed  Loads  Not  Overlapping.  Fig.  83 
illustrates  a  beam  with  one  uniformly  distributed  load  on  part  of  its 
length  and  another  load  on  the  remainder,  as  shown.  The  total  load 
on  the  beam  is 


14X  600  = 
7X1000  = 


8400 
7000 


Total  load  =  15,400# 


STEEL  CONSTRUCTION  91 

Moments  about  Rt  are 

7  X8400  =  58,800 
17|X700Q  =  122,500 


Therefore  1 

Moments  about  R2  are 


181,300  ft.-lb. 
181,300 


3^X7000  =  24,500 
14  X8400  =  117,600 


142,100  ft.-lb 
Therefore  Rl  = *     '  =  6767  # 

7?1+fl2=6767+8633  =  15,400# 

fi7fi7 

Maximum  shear  is  8633.    Zero  shear  occurs  at  a  point  or 

OUU 

11.28  feet  to  the  right  of  7?t.    Hence  this  is  the  point  of  maximum 
bending  moment. 

The  bending  moment  computed  on  the  right  is 
+9.72X8633  +83,913 

_2iZ?X2. 72X600=-    2220 
2 

-6.22X7000          =-43,540     -45,760 

+38,153  ft.-lb. 

The  bending  moment  computed  on  the  left  is 
+11.28X6767  =+76,332 

~^pXll.  28X600=  -38,166 

+38,166  ft.-lb. 

Two  Distributed  Loads  and  Concentrated  Loads.  Fig.  84  illus- 
trates a  beam  with  one  uniformly  distributed  load  for  part  of  its 
length,  another  load  for  the  remainder,  and  a  concentrated  load  as 
shown.  The  total  load  on  the  beam  is 

u.d.  12X1,000  =  12,000 
u.d.  4X  500=  2,000 
concentrated  =  10,000 

Total  load         =24,000# 


92  STEEL  CONSTRUCTION 

Moments  about  Rl  are 


6X12,000=  72,000 
12X10,000  =  120,000 
14  X  2,000=  28,000 


220,000  ft.-lb. 


Therefore 


Fig.  84.     Simple  Beam  with  Mixed  Loads 

Moments  about  7?,  are 


_  220,000 
16 


=  13,750$ 


-  16-0 


2X  2,000=  4,000 
4X10,000=  40,000 
10X12,000  =  120,000 

164,000  ft.-lb. 
*i  =  !6MOO  =  10,250# 

Maximum  shear  is  1 3,750  #• 
Zero  shear  occurs  at  10.25  feet 
from  /?,.  Hence  this  is  the 
point  of  maximum  bending  mo- 
ment. 

The  bending  moment  com- 
puted on  the  left  is 

+  10.25  X  10,250  =+105,062 
-  5.125X10,250=-  52,531 

52,531 
ft.-lb. 

-J    This  value  is  to  be  checked  by 
T    computing  the  bending  moment 


.Fig.  85.     Simple  Beams  with  Variable  Loads        on  the  right. 

EXAMPLES  FOR  PRACTICE 

1.  Compute  the  bending  moments  for  the  loads  illustrated  in 
Fig.  85.    Compare  results  with  a  uniformly  distributed  load. 

2.  A  beam  20  feet  long  supports  a  load  of  250  pounds  on  the 
first  5  feet,  400  pounds  on  the  second  5  feet,  and  350  pounds  on  the 


STEEL  CONSTRUCTION  93 

remainder.  What  is  the  maximum  shear?  What  is  the  position  of 
the  maximum  bending  moment? 

3.  What  is  the  bending  moment  on  an  I-beam  15' X42#X30 
feet  long,  due  to  its  own  weight  and  to  a  load  of  14,000  pounds  con- 
centrated at  mid-span? 

Typical  Loadings.  Tabular  Data.  When  the  shear  and  the 
bending  moment  can  be  expressed  in  simple  formulas,  it  is  easier  to 
compute  from  the  formulas  than  from  the  detailed  calculations  just 
illustrated.  Table  II  has  been  compiled  fop  this  purpose.  It  gives 
the  common  arrangements  of  loading  and  the  formulas  for  end  reac- 
tions and  maximum  bending  moment  for  each  case. 

Column  1  gives  diagrams  of  the  arrangement  of  the  loading. 

Columns  2  and  3  give  the  end  reactions  which,  for  all  the  cases 
given,  are  the  same  as  the  end  shears.  When  the  loading  is  sym- 
metrical, the  reaction  is  the  same  at  both  ends  and  is  one-half  the 
total  load.  When  not  symmetrical,  the  values  differ  at  the  two 
ends  and  both  are  given. 

Column  4  gives  the  maximum  bending  moment. 

Column  5  gives  the  distance  in  feet  from  the  left  support  to 
the  point  of  maximum  bending  moment. 

The  symbols  used  are: 

W  =  total  uniformly  distributed  or  variable  loads  in  pounds 

P   =  single  concentrated  load  in  pounds 

L   —  span  in  feet 

Lj  =  distance  from -support  to  center  of  gravity  of  load  on  canti- 
lever beams 

M  =  bending  moment  in  foot-pounds 

/?!  =  reaction  at  left  support 

/?2  =  reaction  at  right  support 

X  =  distance  from  left  support  to  position  of  maximum  bending 
moment 

Simple  Loads.  When  a  load  on  a  simple  beam  is  symmetrically 
placed,  whether  uniformly  distributed  or  concentrated,  the  reac- 
tions are  equal,  and  the  maximum  bending  moment  is  at  the  center 
of  the  span. 

For  a  simple  beam,  irrespective  of  the  manner  of  loading,  the 
maximum  bending  moment  and  zero  shear  occur  at  the  same  point. 


94  STEEL  CONSTRUCTION 

TABLE  II 
Reactions  and  Bending  Moments  for  Typical  Loadings 


rORM  OF  LOAD 


MAXIMUM 
B£HDIN6 
MOMENT 


{w 


w 


jw 


w 


BE  fi  DING  MOM  CUT 
COHSTAHT  OVER 
UNLOADED  PART 


$  w 


tw 


L2    L 


I  W 


2  W 


&W  L 


15 


fiWL 

roWL 


THE  CURVE  IS  A  PAR 
ABOLA.  THE  B.M.  IS 
APP/TOX.  CORRECT  FOR 
CIRCULAR  SEGMENT 


STEEL  CONSTRUCTION 


95 


TABLE  ll-<Continued) 
Reactions  and  Bending  Moments  for  Typical  Loadings 


FORM  OF  LOAD 

», 

». 

MAXIMUM 
BEHD1NG 
MOMENT 

X 

REMARKS 

Lbs, 

Lbs. 

Faof-Lbs. 

16 

f 

KZ 

t' 

i  p 

t". 

i  i- 

POSITION  OF  ONE 
COftCENTRA  TED  LCA- 
FOR  MAXIMlfrl 
BENDING  MOMENT 

f*    jf 

A 

17 

\P 

If 

3  r 

frt 

*<- 

'UJ 

18 

r 

£ 

P 

p 

j  r  L 

H* 

BE  H  DIN  6  MOMENT 
CONSTANT 
BETWEEN  LOADS 

*\  *  \ 

19 

r 

^ 

f>' 

t  r 

g't 

^ 

"^d 

20 

r 

p 

**• 

t> 

i"- 

iL 

*^  j< 

21 

r  -  r  i 

P 

P 

t** 

fr* 

BENDING  MOMENT 
CONSTANT 
BETWEEN  LOADS 

*\  r  \        4 

te 

f  j 

p-f 

'  t' 

t"f 

trL. 

t  L 

je 

25 

X   ,P 

D      S 

n-tn 

r^f) 

p,            rf 

H 

POSITION  Of  TWO 

conceriTRA  JED  L  OADS 

FOX  MAXIMUM 
BE  H  DING  MOMENT 

I 

» 

&m 

?(  WL 

24 

w 

V 

O 

25 

9                    I 

w 

WL, 

0 

3        /./ 

1-          A 

26 

i     gw^ 

w 

WL, 

0 

L^-J 

27 

in 

pi   —  ~rrr> 

1 

w 

jf  W  L 

o 

28 

^^^_ 

w 

iwu 

o 

b-^i^/. 

29 

1 

r 

p 

r.L 

o 

i 

30 

mttm  LI  ,  i  ^ 

r 

P    Ir! 

o 

i 

96  STEEL  CONSTRUCTION 

The  point  of  zero  shear  is  important  only  as  the  easiest  means  of 
locating  the  place  of  maximum  bending  moment. 

For  a  cantilever  beam,  irrespective  of  the  manner  of  loading,  the 
maximum  bending  moment  and  maximum  shear  occur  at  the  sup- 
port. 

Illustrative  Examples.  To  illustrate  the  use  of  Table  II,  assume 
a  beam  18  feet  long  to  be  loaded  from  the  left  support  to  the  middle 
at  320  pounds  per  lineal  foot. 

W  =9X320   =  2880# 
^  =  ^  =  1^  =  1x2880  =  2160# 

72  =  jR,  =  ifF  =  iX2880  =  720  # 

M  =  £  WL    =  £  X28SOX 18  =  7290  ft.-lb. 

Moving  Loads.  It  is  sometimes  necessary  to  know  what  posi- 
tion of  a  moving  load  will  produce  the  maximum  bending  moment  in 
a  beam.  If  it  is  a  single  concentrated  load,  the  maximum  occurs 
when  the  load  is  at  the  center  of  the  span,  as  in  item  16.  Compare 
items  16,  17,  and  19.  If  there  are  two  concentrated  loads,  as  the 
wheels  of  a  traveling  crane,  the  position  producing  the  maximum  is 
shown  in  item  23.  As  there  indicated,  one  load  is  j  D  distant  on 
one  side  of  the  center  of  the  span  and  the  other  is  f  D  distant  on  the 
other  side.  The  maximum  bending  moment  is  at  the  load  nearer 
to  the  center. 

Illustrative  Example.  Assume  two  crane  wheels  spaced  8  feet 
centers,  each  loaded  with  10,000  pounds,  span-  20  feet,  to  find  maxi- 
mum bending  moment.  From  the  formulas 

#1  =  8,000#  and  fl2=12,000#;     Z  =  8  ft. 
Max.  M  =  8X8000  =  64,000  ft.-lb. 

Beam  with  Two  or  More  Loadings.  A  beam  may  have  two  or 
more  of  the  loadings  illustrated.  The  respective  reactions  for  the 
combined  loads  are  the  sums  of  the  corresponding  reactions  for  the 
separate  loadings.  This  applies  in  all  cases.  The  maximum  bend- 
ing moment  for  the  combined  loads  is  the  sum  of  the  moments  for 
the  separate  loadings,  provided  the  positions  of  the  maximums  for 
the  separate  loadings  are  the  same.  Generally  this  condition  occurs 
only  when  all  the  loads  are  symmetrical  about  the  center  of  the 
span,  or  for  cantilever  beams. 


STEEL  CONSTRUCTION  97 

EXAMPLES  FOR  PRACTICE 

1.  What  is  the  bending  moment  of  a  concentrated  load  of 
89,000  pounds  at  the  center  of  a  span  21'-G"  long? 

2.  What  are  the  shear  and  bending  moment  of  a  load  of  21,000 
pounds  at  the  quarter  point  of  a  span  19  feet  long? 

3.  A  beam  is  loaded  at  750  pounds  per  lineal  foot  on  the  two 
end-thirds.     What  is  the  bending  moment? 

4.  A  beam  carries  a  uniformly  distributed  load   of   18,000 
pounds  and  a  center  load  of  9000  pounds.     Span  16  feet.    What 
arc  the  reactions  and  maximum  bending  moment? 

5.  A  crane  girder  has  a  span  of  20  feet.     The  wheel  load  is 
[  30,000  pounds.    The  wheel  base  is  10  feet.     What  is  the  position  of 

loads  for  maximum  bending  moment?    What  is  the  amount  of  the 
maximum  bending  moment? 

CALCULATION  OF  RESISTANCE 

Factors  Considered.  Having  determined  the  shear  and  bending 
^moment  to  which  a  beam  is  subjected,  the  next  step,  logically,  is  to 

•'determine  the  dimensions  of  the  section  wThich  will  resist  them. 

I  The  resistance  to  bending  is  first  provided  for,  as  this  usually  governs 
in  the  design  of  the  rolled  beam  section.  Then  the  shearing  resist- 
ance is  compared  with  the  shearing  stress  to  make  sure  that  it  is 
sufficient.  To  investigate  the  resisting  moment  in  complete  detail 
would  require  the  following  operations: 

(1)  Assume  maximum  unit  stress  on  extreme  fiber 

(2)  Assume  section  of  beam,  and  compute  its  moment  of  inertia 

(3)  From   these  values  compute   the  resisting  moment  of  the 

assumed  section 

(4)  Compare  this  resisting  moment  with  the  bending  moment 

(5)  Repeat  the  operation  until  a  resisting  moment  is  found  which 

equals  or  slightly  exceeds  the  bending  moment 

This  procedure,  with  some  additional  steps,  is  followed  in  the 
case  of  riveted  beams,  but  for  rolled  beams  the  tables  in  the  hand- 
books and  elsewhere  give  resisting  moments  and  various  other 
properties  of  the  sections  so  that  the  operations  are  much  simplified. 

Resisting  Moment.  The  resisting  moment  of  any  beam  is 
determined  from  the  formula 


98  STEEL  CONSTRUCTION 

as  stated  on  p.  78  and  demonstrated  under  Resisting  Moment  in 
"Strength  of  Materials"  Part  I.  This  formula  may  be  changed  to 
the  form 

I^M 
c     S 
which  stated  in  words  is 

moment  of  inertia  _  resisting  moment 
one-Mf  the  depth  unit  stress 

Section  Modulus.    In  the  expression  just  given  -  is  called  the 

c 

"section  modulus,"  (p.  39).  Its  values  for  I-beams,  channels,  and 
angles  are  given  in  the  handbook.  Since  the  resisting  moment  must 
be  equal  to  or  greater  than  the  bending  moment  and,  since  the  value 
of  the  unit  stress  has  been  established,  the  value  of  the  section 
modulus  can  be  computed  and  the  section  selected  from  the  tables. 
For  example,  the  allowable  unit  stress  in  bending  on  the  extreme 
fiber  is  16,000  pounds  per  square  inch;  assume  a  beam  subjected 
to  a  bending  moment  of  100,000  foot-pounds;  since  the  section 
modulus  is  in  terms  of  inches,  the  bending  moment  must  be  expressed 
in  inch-pounds  and  for  this  case  becomes  1,200,000  inch-pounds; 
then  the  section  modulus  required  is 

I_M_  1,200,000    ^eA 

c~~  S~    16,000    = 

Referring  to  the  tables  for  I-beams  it  is  found  that  the  section  having 
the  nearest  higher  value  of  the  section  modulus  is* 

15"  I  60 # 
Expressed  In  simple  words  the  operations  are: 

(1)  Multiply  the  bending  moment  of  the  beam  by  12  to  reduce  it  to  inch-pounds. 

(2)  Divide  this  by  16,000  to  determine  the  required  section  modulus. 

(3)  From  the  tables  select  a  section  whose  section  modulus  is  equal  to  or  greater 

than  the  required  value. 

Tabular  Values  for  Resisting  Moments.  For  a  given  unit  stress 
each  section  has  a  definite  resisting  moment  which  is  computed  from 
the  formula 

M=S~ 
c 

The  values  of  the  resisting  moment  are  not  given  in  all  of  the  hand- 


STEEL  CONSTRUCTION  99 


books.  They  are  given  in  Table  III,  based  on  a  unit  stress  of  16,000 
pounds  per  square  inch,  and  expressed  in  foot-pounds.  This  shortens 
the  operation  of  selecting  a  section,  it  being  necessary  only  to 
choose  a  section  whose  resisting  moment  is  equal  to  or  greater  than 
the  bending  moment  produced  by  the  load  on  the  beam. 

For  example,  assume  a  bending  moment  of  30,625  foot-pounds. 
Referring  to  Table  III,  the  beam  having  the  nearest  higher  resisting 
moment  is  10"  I  25  #,  whose  resisting  moment  is  32,500  foot-pounds. 

If  the  load  on  the  beam  is  uniformly  distributed,  the  compu- 
tations may  be  still  further  shortened  by  means  of  tables  given  in 
the  handbooks.  These  tables  give  the  safe  loads  uniformly  dis- 
tributed for  various  lengths  of  spans.  The  Carnegie  handbook  has 
formerly  given  these  values  for  I-beams,  channels,  angles,  tees,  and 
zees  in  tons  but  in  the  1913  edition  they  are  given  in  thousands  of 
pounds.  The  Cambria  handbook  gives  the  values  for  I-beams  and 
channels  only  and  expresses  them  in  pounds.  For  example,  a  beam 
20  feet  long  supports  a  load  of  700  pounds  per  lineal  foot.  The  total 
load  is  20  X  700=  14,000  #.  From  the  tables  the  size  of  beam  is 
found  to  be  10"  I  30  #. 

EXAMPLES  FOR  PRACTICE 

1.  Two  angles  are  required  to  support  a  load  of  4200  pounds 
uniformly  distributed  on  a  span  of  6  feet.     Determine  the  section, 
by  means  of  the  section  modulus. 

2.  A  channel  having  a  span  12'-6"  long  is  required  to  support 
a  concentrated  load  of  17,900  pounds  at  the  middle  point.    What 
section  is  required? 

3.  Determine  the  sizes  of  beams  required  for  the  conditions 
given  in  the  problems  on  p.  97.     Use  the  simplest  of  the  three 
methods  given  above,  and  check  the  results  by  one  of  the  other 
methods. 

Application  of  Tables  to  Concentrated  Loads.  By  careful 
study  of  the  moment  factors  given  in  Table  II,  the  designer  can 
adapt  the  tables  in  the  handbooks  for  uniformly  distributed  loads 
to  other  forms  of  loading.  Thus  a  concentrated  load  at  the  center 
of  a  span  produces  the  same  bending  moment  as  a  uniformly  dis- 
tributed load  of  twice  the  amount;  then  to  use  the  table  select  a 
beam  whose  capacity  is  twice  the  amount  of  the  concentrated  load. 


100 


STKICL  CONSTRUCTION 


TABLE  III 
Strength  of  Beams 

I-Beams;  H-Sections;  Channels;  Angles;  and  Tees 


Moment 
of 

Section 
Modulus 

Resisting 
Moment 
Based  on 

Shearing 
Resistance 
of  Web 

Strength 
of 
Standard 
End  Con- 

Extreme Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-360  .Span 

Extreme  Length 
for  Beams  without 
Lateral  Support 

I 

I_ 

G 

erf  18,000 

Lb.  per 
Sq.  Inch 

at  10.000 
Lb.  per 
Sq.  Inch 

nections 
American 
Bridge 

For 
Uniformly 
Distrib- 

For 
Center 
Load 

When 
Loaded 
to  Full 

When 
Loaded 
to  Half 

Co..  1911 

uted  Load 

Capacity 

Capacity 

(In.)* 

(In.)' 

Ft.-Lb. 

Pounds 

Pounds 

Ft.    In. 

Ft.  In. 

Ft.    In. 

Ft     In 

27"!    S3# 

2888.6 

214.0 

285,300 

114,500 

54-0 

36-0 

12-  6 

37-6 

24'  I  115# 

2955.5 

2463 

328,400 

180,000 

f>3,000 

48-0 

32-0 

13-  4 

40-0 

110 

2883.5 

240.3 

320,400 

165,100 

' 

13-  3 

39-0 

105 

2811.5 

234.3 

312,400 

150,000 

1 

13-  1 

39-4 

100 

2380.3 

198.4 

264,500 

181,000 

1 

12-  1 

36-3 

95 

2309.6 

192.5 

256,700 

166,100 

1 

12-  0 

36-0 

90 

2239.1 

186.5 

248,800 

151,400 

' 

11-11 

35-8 

85 

2168.6 

180.7 

240,900 

136,800 

1 

11-  9 

35-4 

80 

2087.9 

174.0 

232,000 

120,000 

' 

11-  8 

35-0 

69* 

1928.0 

160.7 

214,300 

93,600 

43,900 

11-  8 

35-0 

21'l57i# 

1227.5 

116.9 

155,900 

75,000 

33,400 

42-0 

28-0 

10-10 

32-6 

20*  I  100# 

1655.8 

165.6 

220,800 

176,800 

44,200 

40-0 

26-8 

12-  2 

36-5 

95 

1606.8 

160.7 

214,300 

162,000 

" 

" 

12-  0 

36-1 

90 

1557.8 

158.5 

207,700 

147,400 

" 

11 

11 

11-11 

35-8 

85 

1508.7 

150.9 

201,200 

132,600 

" 

" 

11-  9 

35-4 

80 

1466.5 

146.7 

195,600 

120,000 

" 

" 

" 

11-  8 

35-0 

75 

1268.9 

126.9 

169,200 

129,800 

" 

" 

" 

10-  8 

32-0 

70 

1219.9 

122.0 

162,700 

115,000 

«. 

" 

11    . 

10-  7 

31-8 

65 

1169.6 

117.0 

156,000 

100,000 

" 

" 

" 

10-  5 

31-3 

IS*  I    90# 

1260.4 

140.0 

186,700 

145,300 

43,100 

36-0 

24-0 

12-  1 

36-  3 

85 

1220.7 

135.6 

180,800 

130,500 

" 

" 

" 

11-11 

35-10 

80 

1181.0 

131.2 

175,000 

115,900 

" 

M 

M 

11-10 

35-  5 

75 

1141.3 

126.8 

169,100 

101,200 

" 

" 

" 

11-  8 

35-  0 

70 

921.3 

102.4 

'  136,500 

129,400 

" 

" 

" 

10-  5 

31-  4 

65 

881.5 

97.9 

130,500 

114,700' 

" 

" 

" 

10-  4 

30-11 

60 

841.8 

93.5 

124,700 

99,900 

" 

11 

" 

10-  2 

30-  6 

55 

795.6 

88.4 

117,900 

82,800 

" 

" 

" 

10-  0 

30-  0 

46 

733.2 

81.5 

108,700 

58,000 

30,200 

" 

11-  8 

35-  0 

15"  I  100# 

900.5 

120.1 

160,100 

177,600 

35,400 

30-0 

20-0 

11-  3 

33-10 

95 

872.9 

116.4 

155,200 

162,800 

" 

" 

11-  1 

33-  4 

90 

845.4 

112.7 

150,300 

148,000 

" 

" 

11 

11-  0 

32-11 

85 

817.8 

109.0 

145,300 

133,400 

" 

" 

10-  9 

32-  4 

80 

795.5 

106.1 

141,500 

121,500 

" 

" 

" 

10-  8 

32-  0 

75 

691.2 

92.2 

122,900 

132,300 

" 

" 

" 

10-  6 

31-  5 

70 

663.6 

88.5 

118,000 

117,600 

" 

" 

" 

10-  4 

31-  0 

65 

636.0 

84.8 

113,100 

102,900 

11 

11 

" 

10-  2 

30-  6 

60 

609.0 

81.2 

108,300 

88,500 

M 

.  " 

" 

10-  0 

30-  0 

55 

511.0 

68.1 

90,800 

98,400 

" 

" 

" 

9-  7 

28-9 

50 

483.4 

64.5 

86,000 

83,700 

" 

" 

" 

9-  5 

28-  3 

45 

455.8 

60.8 

81,100 

69,000 

" 

" 

" 

9-  3 

27-  9 

42 

441.7 

58.9 

78,500 

61,500 

" 

" 

" 

9-  2 

27-  6 

3S 

405.1 

54.1 

72,000 

43,400 

32,500 

" 

" 

9-  2 

27-  6 

STKK1. 

TABLED  III  (Cpr.tinueJt 
Strength  of  Beams 

I -Beams;  H -Sections;  Channels;  Angles;  and  Te< 


SECTION 

Moment 
of 
Inertia 

Section 
Modulus 
I 
c 

Resisting 
Moment 
Based  on 
Unit  Str.-ss 
of  16.000 
Lh.  per 
Sq.  Inch 

Shearing 
Resistance 
of  Web 
at  10.000 
Lb.  per 
Sq.  Inch 

Strength 

Standard 
End  Con- 
nections 
American 
Bridge 
Co..  1911 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-360  Span 

Extreme  Length 
for  Beams  without 
Lateral  Support 

For 
Uniformly 
Distrib- 
uted Load 

For 
Center 
Load 

When 
Loaded 
to  Full 
Capacity 

When 
Loaded 
to  Half 
•Capacity 

(In.)< 

(In.)3 

Ft.-Lb. 

Pounds 

Pounds 

Ft.    In. 

Ft.  In. 

Ft.    In. 

Ft.    In. 

12*  I  55# 
50 
45 
40 
35 
311 
27* 

321.0 
303.3 

285.7 
268.9 
228.3 
215.8 
199.6 

53.5 
50.6 
47.6 
44.8 
38.0 
36.0 
33.3 

71,300 
67,500 
63,500 
59,700 
50,700 
48,000 
44,400 

98,600 
83,900 
69,100 
55,200 
52,300 
42,000 
38,200 

26,500 
23,900 

24-0 

16^0 

9-  4 
9-  2 
8-11 
8-  9 
8-6 
8-  4 
8-4 

28-  1 
27-  5 
26-10 
26-  3 
25-5 
25-  0 
25-  0 

10"  I  40# 
35 
30 
25 
22 

158.7 
146.4 
134.2 
122.1 
113.9 

31.7 
29.3 
26.8 
24.4 

22.8 

42,300 
39,100 
35,700 
32,500 
30,400 

74,900 
60,200 
45,500 
31,000 
23,200 

17,700 
17,400 

20-0 

\3r-4 

8-6 
8-3 
8-0 
7-9 
7-9 

25-6 
24-9 
24-0 
23-4 
23-4 

9"I35# 
30 
25 
21 

111.8 
101.9 
91.9 
84.9 

24.8 
22.6 
20.4 
18.9 

33,100 
30,100 
27,200 
25,200 

65,900 
51,200 
36,500 
26,100 

17,700 

18^0 

12-0 

7-11 
7-  8 
7-  5 
7-  3 

23-10 
23-  0 
22-  3 
21-  8 

8'  I  25J# 
23 
20J 
18 
17* 

68.4 
64.5 
60.6 
56.9 
58.3 

17.1 
16.1 
15.1 
14.2 
14.6 

22,800 
21,400 
20,100 
18,900 
19,500 

43,300 
35,900 
28,600 
21,600 
16,800 

17,700 
15,800 

16K) 

10j8 

7-  1 
7-0 
6-10 
6-  8 
7-  3 

21-  4 
20-11 
20-  5 
20-  0 
21-  8 

7"I20# 
17} 

15 

42.2 
39.2 
36.2 

12.1 
11.2 
10.4 

16,100 
14,900 
13,900 

32,100 
24,700 
17,500 

17,700 

14-0 

9-4 

6-5 
6-3 
6-1 

19-  4 
18-10 
18-  4 

6'117i# 
14! 

124 

26.2 
24.0 
21.8 

8.7 
8.0 
7.3 

11,600 
10,700 
9,700 

28,500 
21,100 
13,800 

8,800 
8,600 

12-0 

8-0 

7-2 
5-9 
5-7 

21-5 
17-3 
16-8 

5'  I  14i# 
12} 
91 

15.2 
13.6 
12.1 

6.1 

5.4 

4.8 

8,100 
7,200 
6,400 

25,200 
17,800 
10,500 

8,800 
7,900 

10-0 

6-8 

5-6 
5-3 
5-0 

16-6 
15-9 
15-0 

4"I10J# 
9* 

•11 

7.1 
6.7 
6.4 
6.0 

3.6 
3.4 
3.2 
3.0 

4,800 
4,500 
4,300 
4,000 

16,400 
13,500 
10,500 
7,600 

8,800 
7,100 

8yO 

5r-4 

4-10 
4-  8 
4-  7 
4-  5 

14-5 
14-0 
13-8 
13-4 

3'I    7*# 

2.9 
2.7 
2.5 

1.9 
1.8 
1.7 

2,500 
2,400 
2,270 

10,800 
7,900 
5,100 

8,800 
6,400 

6jO 

4^0 

4-  T 
4-0 
3-11 

12-7 
12-1 
11-8 

H-8'-34.0# 
6'-23.8 
5M8.7 
4M3-6 

115.4 
45.1 
23.8 
10.7 

28.9 
15.0 
9.5 
5.3 

38,500 
20,000 
12,700 
7.100 

30,000 
18,800 
15,600 

12,500 

| 

13-4 
12-0 
10-0 

8-0 

10-8 
8-0 
6-8 
5-4 

— 

- 

102  STHKL    roXSTRTCTlON 

TABLE  III.  (Continued) 
Strength  of  Beams 

I -Beams;  H -Sect ions;  Channels;  Angles;  and  Tees 


SECTION 

Moment 
cf 
Inertia 

I 

Section 

Modulus 

_L 

c 

Resisting 
Moment 
Based  ou 
Unit  Stress 
of  16.000 
Lb.  per 
Sq.  Inch 

Shearing 
Resistance 
of  Web 
at  10,000 
Lb.  per 
.Sq.  Inch 

Strength 
of 
Ftandard 
End  Con- 
nections 
American 
Bridge 
Co.,  1911 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-360  Span 

Extreme  Length 
for  Beams  without 
Lateral  Support 

For 
Uniformly 
Distrib- 
uted Load 

Center 
Load 

When 
Loaded 
to  Full 
Capacity 

When 
Loaded 
to  Half 
Capacity 

(In.)* 

(In.)' 

Ft.-Lb. 

Pounds 

Pounds 

Ft.    In. 

Ft.  In. 

Ft.    In. 

Ft      In. 

15*  C  55# 
40 
45 
40 
35 
33 

430.2 
402.7 
375.1 
347.5 
320.0 
312.6 

57.4 

53.7 
50.0 
46.3 
42.7 
41.7 

76,500 
71,600 
66,700 
61,700 
56,900 
55,600 

122,700 

108,000 
93,300 
78,600 
63,900 
60,000 

35^400 
<t 

3(H) 

20jO 

6-  4 
6-  2 
6-  0 
5-11 
5-  9 
5-  8 

19-1 
18-6 
18-1 
17-7 
17-2 
17-0 

12"  C  40# 
35 
30 
25 
20J 

197.0 
179.3 
161.7 
144.0 
128.1 

32.8 
29.9 
26.9 
24.0 
21.4 

43,700 
39,900 
35,900 
32,000' 
28,500 

91,000 
76,300 
61,600 
46,800 
33,600 

26,500 
26,200 

24-0 

16-0. 

5-  8 
5-  6 
5-  3 
5-  1 
4-11 

17-  1 
16-  6 
15-10 
15-  3 
14-  8 

10'  L  35# 
30 
25 
20 
15 

115.5 
103.2 
91.0 

78.7 
66.9 

23.1 
20.6 
18.2 
15.7 
13.4 

30,800 
27,500 
24,300 
20,900 
17,900 

82S,300 
67,600 
52,900 
38,200 
24,000 

17,700 

20-0 

13-4 

5-  4 
5-  1 
4-10 
4-  7 
4-  4 

15-11 
15-  2 
14-  5 
13-  9 
13-  0 

9"C25# 
20 
15 
13| 

70.7 
60.8 
50.9 
47.3 

15.7 
13.5 
11.3 
10.5 

20,900 
18,000 
15,100 
14,000 

55,400 
40,700 
25,900 
20,700 

17,700 
17,200 

18jO 

12-0 

4-8 
4-5 
4-2 
4-1 

14-1 
13-3 
12-5 
12-2 

8*  C2H# 
18| 
161 
13f 
111 

47.8 
43.8 
39.9 
36.0 
32.3 

11.9 
11.0 
10.0 
9.0 

8.1 

15,900 
14,700 
13,300 
12,000 
10,800 

46,600 
39,200 
31,900 
24,600 
17,600 

17,700 
16,500 

16^0 

10-8 

4-  4 
4-  3 
4-  1 
3-11 
3-  9 

13-1 
12-8 
12-2 
11-9 
11-4 

7"  C  19-# 

m 

142 
12] 
9| 

33.2 
30.2 
27.2 
24.2 
21.1 

9.5 
8.6 
7.8 
6.9 
6.0 

12,700 
11,500 
10,400 
9,200 
8,000 

44,300 
37,000 
29,600 
22,300 
14,700 

17,700 
15,800 

14-0 

9-4 

4-  2 
4-  0 
3^10 
3-  8 
3-  6 

12-7 
12-0 
11-6 
11-0 
10-5 

6"  L  15£# 
13 

m 

19.5 
17.3 
15.1 
13.0 

6.5 
5.8 
5.0 
4.3 

8,700 
7,700 
6,700 
5,700 

33,800 
26,400 
19,100 
12,000 

8,800 
7,500 

12-0 

SyO 

3-10 
3-  7 
3-  5 
3-  2 

11-  5 
10-10 
10-  2 
9-  7 

5-E11J* 
6} 

10.4 
8.9 

7.4 

4.2 
3.5 
3.0 

5,600 
4,700 
4,000 

23,800 
16,500 
9,500 

8,800 
7,100 

10-0 

6-8 

3-  5 
31  2 
2-11 

10-2 
9-5 
8-9 

"T 

4.6 
4.2 
3.8 

2.3 
2.1 
1.9 

3,100 
2,800 
2,500 

12,000 
10,100 
7,200 

8,800 
6,800 

8^0 

5-4 

2-10 
2-  9 
2-  8 

8-  7 
8-3 
7-11 

3"C    6# 
5 
4 

2.1 
1.8 
1.6 

1.4 
1.2 
1.1 

1,870 
1,600 
41,70 

10,900 
7,900 
5,100 

8,800 
6,400 

.67° 

4-0 

2-8 
2-6 

2-4 

8-0 
7-6 
7-1 

STEEL  CONSTRUCTION 

TABLE  III   (Continued) 

Strength  of  Beams 

I-Beams;  H-Sections;  Channels;  Angles;  and  Tees 


103 


Extreme  length 

Extreme  length 

Mom- 

Sec- 
tion 

Resisting 
Moment 
Based  on 
Unit 

for  Deflection 
for  Plastered 
Ceilings,  Limit 
1-480  Span 

Mom- 

Sec- 
tion 
Modu- 

Resisting 
Moment 
Based  on 

for  Deflection 
for  Plastered 
Ceilings,  Limit 
1-480  Span 

SECTION 

Inertia 

lus"" 

Stress 

For  Un- 

SECTION 

Inertia 

lus 

Stress 

For  Un- 

I 

of  16.000 

iformly 

For 

I 

of  16.000 

iformly 

For 

I 

~c~ 

Lb.  per 

Distrib- 

Center 

I 

Lb.  per 

Distrib- 

Center 

Sq.  Inch 

uted 

Load 

Sq.  Inch 

uted 

Load 

Load 

Load 

(InJ« 

(In.)« 

Ft.-Lb. 

Ft.  In. 

Ft.  In. 

(In.)< 

(In.)3 

Ft.-Lb. 

Ft.  In. 

Ft.  In. 

L-8x8xli 
1A 

97.97 
93.53 

88.98 

17.53 
16.67 
15.80 

23,400 
22,200 
21,100 

•17-0 

11-0 

L'3SX3it 

3.99 
3.64 
3.26 

1.65 
1.49 
1.32 

2,200 

1,990 
1,760 

7-0 

4-9 

H 

34.33 

14.91 

19,900 

4t 

" 

1 

2.87 

1.15 

1,530 

" 

i 

79.58 
74.71 

14.01 
13.11 

18,700 
17,500 

« 

L-3x3x  H 

2.45 
2.81 

0.98 
1.40 

1,310 
1,870 

6-0 

4-0 

69.74 

12.18 

16,200 

" 

1 

1 

2.62 

1.30 

1,730 

" 

i 

64.64 
59.42 

11.25 
10.30 

15,000 
13,700 

M 

; 

f 

2.43 
2.22 

1.19 
1.07 

1,590 
1,430 

:; 

V 

54.09 

9.34 

12,500 

11 

" 

A 

1.99 

0  95 

1,270 

" 

i 

48.63 

8.37 

11,200 

M 

M 

i 

1.76 

0.83 

1,110 

" 

L-6x6xl 

35.46 

8.57 

11,400 

12-6 

8-6 

1.51 

0.71 

950 

« 

H 

33.72 

8.11 

10,800 

" 

" 

i 

1.24 

0  58 

770 

" 

31.92 

7.64 

10,200 

<< 

M 

L-<?ax2|xi 

1.67 

0.89 

1,190 

5-9 

3-9 

I3 

30.06 
28  15 

7  15 
6.66 

9,500 
8,900 

" 

M 

f 

1.51 
1  33 

0.79 
0.69 

1,050 
920 

;; 

1* 

26  IP 
24  16 

6  17 
5.66 

8,200 
7,500 

" 

;; 

t 

1.15 
0.93 

0.59 
0  48 

790 
640 

(, 

A 

22.07 

5.14 

6,800 

' 

" 

L-2jx23xA 

1.34 

0  80 

1,070 

5-0' 

3-4 

I 

19.91 

4.61 

6,100 

' 

u 

I 

1.23 

0.73 

970 

" 

A 

17  68 

4.07 

5,400 

' 

" 

A 

1.11 

0.65 

870 

" 

1 

15.39 

3.53 

4,700 

' 

" 

1 

0.98 

0.57 

760 

" 

L-5x5xl 

19.64 

5.80 

7,700 

10-6 

7-0 

A 

0.85 

0  48 

640 

« 

U 

18.71 

5.49 

7,300 

j 

" 

1 

0.70 

0.40 

530 

« 

17  7.5 

5.17 

6,900 

1 

" 

A 

0.55 

0.30 

400 

« 

1 

16.77 

4.85 

6,500 

1 

14 

L-°zX9iX5 

0.87 

0.58 

770 

4-6 

3-0 

15.7-1 

4.53 

6,000 

' 

11 

"  A 

0.79 

0.52 

690 

" 

]l 

14.  & 

4.20 

5,600 

' 

" 

1 

0.70 

0.45 

600 

« 

13.  & 

3.86 

5,100 

1 

" 

A 

0.61 

0.39 

520 

" 

A 

12.44 

3.51 

4,700 

' 

" 

1 

0.51 

0.32 

430 

" 

1 

11.25 

3.15 

4,200 

1 

" 

•A 

0.39 

0.24 

320 

« 

A 

10.02 

2.79 

3,700 

1 

" 

L-2x2xi 

0.59 

0.45 

600 

4-0 

2-9 

L-4x4x  i 

8.74 
8.5P 

2.42 
3.20 

3,200 
4,300 

8-3 

5-6 

t 

0.54 
0.48 

0.40 
0.35 

530 
470 

!! 

I1 

8.14 

3.01 

4,000 

" 

" 

A 

0.42 

0.30 

400 

" 

7.67 

2.81 

3,700 

" 

.    " 

i 

0.35 

0.25 

330 

" 

ji 

7.17 

2.61 

3,500 

" 

" 

0.28 

0.19 

250 

« 

6.66 

2.40 

3,200 

" 

11 

A 

6.12 

2.19 

2,900 

u 

" 

• 

5.56 

1.97 

2,600 

" 

" 

A 

4.97 

1.75 

2,300 

" 

" 

| 

4.36 

1.52 

2,000 

" 

" 

A 

3.71 

1.29 

1,700 

" 

" 

L-3ix3$xJ 

5.53 

2.39 

3,200 

7-0 

4-9 

w 

5.25 

2.25 

3,000 

" 

" 

| 

4.% 

2.11 

2,800 

" 

" 

'H 

4.65 

1.96 

2,600 

" 

" 

1 

4.33 

1.81 

2,400 

" 

104 


STEEL  CONSTRUCTION 

TABLE  III  (Continued) 

Strength  of  Beams 

I-Beams;  H-Sections;  Channels;  Angles;  and  Tees 


LONG  LEO  VERTICAL 

SHORT  LEG  VERTICAL 

SECTION 

Moment 
of 

Section 
Modulus 

Resisting 
Moment 
Based  on 
Unit 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-360  Span 

Moment 
of 

Section 
Modulus 

Resisting 
Moment 
Based  on 
Unit 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-360  Span 

Stress 

I 

Stress 

I 

c 

of  16.000 
Lb.  per 
Sq.  Inch 

Uniformly 
Distrib- 
uted Load 

For 
Center 
Load 

I 

~c~ 

of  16.000 
Lb.per 
Sq.  Inch 

For 
Uniformly 
Distrib- 
uted Load 

For 
Center 
Load 

(In.)< 

(In.)s 

Ft.-Lb. 

Ft.    In. 

Ft.  In. 

(In.)4 

(In.)» 

Ft.-Lb. 

Ft.    In. 

Ft.  In. 

L-8x6xl 

80.78 

15.11 

20,100 

16-3 

10-9 

38.78 

8.92 

11,900 

13-3 

8-9 

il 

76.59 

14.27 

19,000 

11 

44 

36.85 

8.43 

11,200 

44 

72.32 

13.41 

17,900 

4 

41 

34.86 

7.94 

10,600 

" 

•' 

If 

67.92 

12.55 

16,700 

1 

44 

32.82 

7.44 

9,900 

44 

" 

| 

63.42 

11.67 

15,600 

' 

44 

30.72 

6.92 

9,200 

4 

" 

ii 

58.82 

10.77 

14,400 

1 

« 

28.56 

6.40 

8,500 

4 

•t 

1 

54.10 

9.87 

13,200 

1 

11 

26.33 

5.88 

7,800 

4 

tf 

A 

49.26 

8.95 

11,900 

' 

44 

24.04 

5.34 

7,100 

4 

" 

* 

44.31 

8.02 

10,700 

4 

14 

21.68 

4.79 

6,400 

4 

44 

L-7x3Jxl 

45.37 

10.58 

14,100 

12-3 

8-9 

7.53 

2.96 

3,900 

7-9 

5-3 

H 

43.13 

10.00 

13,300 

44 

" 

7.18 

2.80 

3,700 

44 

41 

40.82 

9.42 

12,600 

M 

44 

6.83 

2.64 

3,500 

44 

" 

f 

38.45 

8.82 

11,800 

11 

" 

6.46 

2.48 

3,300 

44 

44 

35.99 

8.22 

11,000 

44 

44 

6.08 

2.31 

3,100 

44 

" 

i 

33.47 

7.60 

10,100 

44 

44 

5.69 

2.14 

2,900 

14 

" 

• 

30.86 

6.97 

9,300 

" 

5.28 

1.97 

2,600 

44 

" 

A 

28.18 

6.33 

8,400 

" 

44 

4.86 

1.80 

2,400 

44 

44 

i 

25.41 

5.68 

7,600 

44 

44 

4.41 

1.62 

2,200 

41 

" 

A 

22.56 

5.01 

6,700 

44 

14 

3.95 

1.47 

1,960 

44 

4< 

L-6x4xl 

30.75 

8.02 

10,700 

11-9 

7-9 

10.75 

3.79 

5,000 

8-6 

5-9 

iH 

29.26 

7.59 

10,100 

44 

44 

10.26 

3.59 

4,800 

44 

44 

-j 

27.73 

7.15 

9,500 

41 

44 

9.75 

3.39 

4,500 

44 

44 

1^ 

26.15 

6.70 

8,900 

11 

44 

923 

3.18 

4,200 

44 

41 

| 

24.51 

6.25 

8,300 

41 

44 

8.68 

2.97 

4,000 

44 

" 

H 

22.82 

5.78 

7,700 

44 

44 

8.11 

2.76 

3,700 

4 

" 

1 

21.07 

5.31 

7,100 

44 

44 

7.52 

2.54 

3,400 

4 

44 

A 

19.26 

4.83 

6,400 

14 

44 

6.91 

2.31 

3,100 

4 

44 

\ 

17.40 

4.33 

5,800 

44 

44 

6.27 

2.08 

2,800 

4 

44 

fi 

15.46 

3.83 

5,100 

41 

44 

5.60 

1.85 

2,500 

4 

44 

I 

13.47 

3.32 

4,400 

44 

44 

4.90 

1.60 

2,100 

44 

" 

L-6x3ixl 

29.24 

7.83 

10,400 

11-8 

7-9 

7.21 

2.90 

3,900 

7-9 

5-3 

ii 

27.84 

7.41 

9,900 

44 

44 

6.88 

2.74 

3,700 

14 

26.38 

6.98 

9,300 

44 

44 

6.55 

2.59 

3,500 

44 

" 

| 

24.89 

6.55 

8,700 

44 

44 

6.20 

2.43 

3,200 

4 

" 

23.34 

6.10 

8,100 

41 

44 

5.84 

2.27 

3,000 

• 

44 

ji 

21.74 

5.65 

7,580 

44 

44 

5.47 

2.11 

2,800 

4 

44 

20.08 

5.19 

6,900 

44 

44 

5.08 

1.94 

2,600 

4 

A 

18.37 

4.72 

6,300 

44 

44 

4.67 

1.77 

2,400 

4 

M 

1 

16.59 

4.24 

5,700 

11 

44 

4.25 

1.59 

2,100 

4 

44 

A 

14.76 

3.75 

5,000 

11 

44 

3.81 

1.41 

1,880 

4 

41 

1 

12.86 

3.25 

4,300 

11 

44 

3.34 

1.23 

1,640 

4 

44 

L-5x4x  i 

16.42 

4.99 

6,700 

10-0 

6-8 

9.23 

3.31 

4,500 

8-6 

5-9 

H 

15.54 

4.69 

6,300 

41 

44 

8.74 

3.11 

4,100 

41 

44 

! 

14.60 

4.37 

5,800 

41 

" 

8.23 

2.90 

3,900 

41 

44 

ti 

13.62 

4.05 

5,400 

44 

14 

7.70 

2.69 

3,600 

44 

44 

1 

12.61 

3.73 

5,000 

<4 

41 

7.14 

2.48 

3,300 

44 

•  4< 

STEEL  CONSTRUCTION 


105 


TABLE  III  (Continued) 
Strength  of  Beams 

I -Beams;  H-Sections;  Channels;  Angles;  and  Tees 


SECTION 

LONG  LEG  VERTICAL 

SHORT  LEG  VERTICAL 

foment 
of 
Inertia 

I 

Section 
Modulus 

_i_ 

Resisting 
•Moment 
Bawd  on 
Unit 
Stress 
of  16.000 
Lb.  per 
Sq.  Inch 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-480  Span 

Moment 
of 
Inertia 

I 

Section 
Modulus 

~c~ 

Resisting 
Moment 
Baaed  on 
Unit 
Stress 
of  16.000 
Lb.  per 
Sq.  Inch 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-480  Span 

For 
I'niformlv 
Distrib- 
ited  Load 

For 
Center 
Load 

For 
Uniformly 
Distrib- 
uted Load 

For 
Center 
Load 

(Ia.)« 

(In.)' 

Ft.-Lb. 

Ft      In. 

Ft.  In. 

(In.)« 

(In.)' 

Ft.-Lb. 

Ft.     In. 

Ft.  In. 

L-5x4x  A 

r 

11.55 
10.46 
9.32 
8.14 

3.39 
3.05 
2.70 
2.34 

4,500 
4,100 
3,600 
3,100 

10-0 

6-8 

6.5G 
5.96 
5.32 
4.67 

2.26 
2.04 
1.81 
1.57 

3,100 

2,700 
2,400 
2,100 

8~^ 

5-9 

L-5x3*x  I 

1* 
I 

I 

15.b7 
14.81 
13.92 
12.99 
12.03 
11.03 
9.99 
8.90 
7.78 
6.60 

4.88 
4.58 
4.28 
3.97 
3.65 
3.32 
2.99 
2.64 
2.29 
1.94 

6,500 
6,100 
5,700 
5,300 
4,900 
4,400 
4,000 
3,500 
3,100 
2,600 

P-9 

,,, 

6-6 

6.21 
5.89 
5.55 
5.20 
4.83 
4.45 
4.05 
3.63 
3.18 
2  72 

2.52 
2.37 
2  22 
2M 
1.90 
1.73 
1.56 
1.39 
1.21 
1.02 

3,400 
3,200 
3,000 
2,700 
2,500 
2,300 
2,100 
1,850 
1,610 
1,360 

7-6 

5r° 

L-5x3x  J| 

F 
r 

i 

13.98 
13.15 
12.28 
11.37 
10.43 
9.45 
8.43 
7.37 
6.26 

4.45 
4.16 
3.86 
3.55 
3.23 
2.91 
2.58 
2.24 
1.89 

5.900 
5,500 
5,100 
4,700 
4,300 
3,900 
3,400 
3.000 
2,500 

9-8 

6-6 

3.71 
3.51 
3.29 
3.06 
2.83 
2.58 
2.32 
2.04 
1.75 

1.74 
1.63 
1.51 
1.39 
1.27 
1.15 
1.02 
0.89 
0.75 

2,300 
2,200 
2,000 
1,850 
1,690 
1,530 
1,360 
1,190 
1,000 

6-8 

4-6 

L-4*x3x  H 
A 

10.33 
9.73 
9.10 
8.44 
7.75 
7.04 
6.29 
5.50 
4.69 

3.62 
3.38 
3.14 
2.89 
2.64 
2.37 
2.10 
1.83 
1.54 

4,800 
4,500 
4,200 
3,900 
3,500 
3,200 
2,800 
2,400 
2,100 

8-9 

5-9 

3.60 
3.40 
3.19 
2.98 
2.75 
2.51 
2.25 
1.98 
1.73 

1.71 
1.60 
1.49 
1.37 
1.25 
1.13 
1.01 
0.88 
0.76 

2,300 
2,100 
1,990 
1,830 
1,670 
1:510 
1,350 
1,180 
1,010 

6-6 

4-4 

L-4x3£x  H 

I 

& 

7.77 
7.32 
6.86 
6.37 
5.86 
5.32 
4.76 
4.18 
3.56 

2.92 
2.75 
2.56 
2.35 
2.15 
1.93 
1.72 
1.50 
1.26 

3,900 
3,700 
3,400 
3,100 
2,900 
2,600 
2,300 
2,000 
1,680 

8^0 

5^6 

5.49 
5.18 
4.86 
4.52 
4.17 
3.79 
3.40 
2.99 
259 

2.30 
2.15 
2.00 
1.84 
1.68 
1.52 
1.35 
1.18 
1.01 

3,100 
2,900 
2,700 
2,500 
2,200 
2,000 
1,800 
1,570 
1,350 

7^6 

5^0 

L-4x3x  J| 

7.34 
6.93 
6.49 
6.03 
5.55 

2.87 
2.68 
2.49 
2.30 
2.09 

3,800 
3,600 
3,300 
3,100 

2,800 

8-0 

5-4 

3.47 
3.28 
3.08 
2.87 
2.66 

1.68 
1.57 
1.46 
1.35 
1.23 

2,200 
2,100 
1,950 
1,800 
1A640 

M 

4-4 

M 

106  STEEL  CONSTRUCTION 

TABLE  III  (Cdntinued) 
Strength  of  Beams 

I-Beams;  H-Sections;  Channels;  Angles;  and  Tees 


6ECTION 

LONG  LEG  VERTICAL 

SHORT  LEO  VERTICAL 

Moment 
Inertia 

Section 
Modulus 

~<f 

Resisting 
.Moment 
Based  on 
Unit 
Stress 
of  16.000 
Lb.  per 
Sq.  Inch 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-480  Span 

Moment 
of 
Inertia 

Section 
Modulus 

"c~ 

Resisting 
Moment 
Based  on 
Unit 
Stress 
of  16,000 
Lb.  per 
Sq.  Inch 

Extreme  Length 
for  Deflection  for 
Plastered  Ceilings 
Limit  1-480  Span 

For 
Un-formlj 
Distri»>- 
uted  Load 

For 
Center 
Load 

For 
Uniformly 
Distrib- 
uted Load 

For 
Center 
Load 

(In.)* 

(In.)» 

Ft.-Lb. 

Ft.    In. 

Ft.  In. 

(In.)4 

(In.)' 

Ft.-Lb. 

Ft.    In. 

Ft.  In. 

L-4x3x  1 

t 

5.05 
4.52 
3.96 
3.38 

1.89 
1.68 
1.46 
1.23 

2,500 
2,200 
1,940 
1,640 

8^0 

5-4 

2.42 
2.18 
.1.92 
1.65 

1.12 
0.99 
0.87 
0.74 

1,490 
1,320 

1,160 

9CO 

6^6 

4-4 

X 

co 

X 

rt 

Jl 

4.98 
4.70 
4.41 
4.11 
3.79 
3.45 
3.10 
2.72 
2.33 

2.20 
2.05 
1.91 
1.76 
1.61 
1.45 
1.29 
1.13 
0.96 

2,900 
2,700 
2,500 
2,300 
2,100 
1,930 
1,720 
1,510 
1,280 

7-0 

4-9 

3.33 
3.15 
2.96 
2.76 
2.55 
2.33 
2.09 
1.85 
1.58 

1.65 
1,54 
1.44 
1.33 
1.21 
1.10 
0.98 
0.85 
0.72 

2,200 
2,100 
1,920 
1,770 
1,610 
1,470 
1,310 
1,130 
960 

C-4 

4-3 

L-3Jx2Jx|* 
& 

f 

4.13 
3.85 
3.55 
3.24 
2.91 
2.56 
2.19 
1.80 

1.85 
1.71 
1.56 
1.41 
1.26 
1.09 
0.93 
0.75 

2,500 
2,300 
2,100 
1,880 
1,680 
1,450 
1,240 
1,000 

6^4 

4-6 

1.72 
1.61 
1.49 
1.36 
1.23 
1.09 
0.94 
0.78 

0.99 
0.92 
0.84 
0.76 
0.68 
0.59 
0.50 
0.41 

1,320 
1,230 
1,120 
1,010 
910 
790 
670 
550 

fr-4 

3-6 

L-3Jx2x  A 

p 

f 

2.64 
2.42 
2.18 
1.92 
1.65 
1.36 

1.30 
1.17 
1.05 
0.91 
0.77 
0.63 

1,730 
1,560 
1,400 
1,210 
1,030 
840 

6-4 

4-3 

0.75 
0.69 
062 
0.55 
0.48 
0.40 

0.53 
~0.48 
0.43 
0.37 
0.32 
0.26. 

710 
640 
570 
490 
430 
350 

4-4 

3-0 

L-3x2£x  A 

f 

2.28 
2.08 
188 
1.66 
1.42 
1.17 

1.15 
1.04 
0.93 
0.81 
0.69 
0.56  . 

1,530 
1,390 
1,240 
1,080 
920 
750 

6^0 

4-0 

1  42 
1.30 
1.18 
1.04 
0.90 
0.74 

0.82 
0.74 
066 
0.58 
0.49 
0.40 

1,090 
990 
880 
770 
650 
530 

4-4 

3-6 

L-3x2x  £ 

IT 

f 

1.92 
1.73 
1.53 
1.32 
1.09 

1.00 
0.89 
0.78 
0.66 
0.54 

1,330 
1,190 
1,040 
880 
720 

5-9 

3-9 

0.67 
0.61 
0.54 
0.47 
0.39 

0.47 
0.42 
0.37 
0.32 
0.25 

630 
560 
490 
430 
330 

4_4 

3-0 

L-2|x2x  *T 
IT 

s 

1.14 
1.03 
0.91 
0.79 
0.65 
0.51 

0.70 
0.62 
0.55 
0.47 
0.38 
0.29 

930 
830 
730 
630 
510 
390 

5-0 

3-4 

0.64 
0.58 
0.51 
0.45 
0.37 
0.29 

0.46 
0.41 
0.36 
0.31 
0.25 
0.20 

610 
550 
480 
410 
330 
270 

4-3 

2-9 

STKKL  CONSTRUCTION 

TABLE  III  (Continued) 
Strength  of  Beams 

I-Beams;  H-Sections;  Channels;  Angles;  and  Tees 


107 


SECTION 

Mom- 
ent of 
Inertia 

I 

Section 
Modu- 
lus 

"c~ 

Resisting 
Moment 
Based  on 
Unit 
Stress 
of  16,000 
Lb.per 
Sq.In. 

Extreme 
Length  for 
Deflection  for 
Plastered 
Ceilings 
Limit  1-180 
Span 

SECTION 

Mom- 
ent for 
Inertia 

I 

Section 
Modu- 
lus 

J_ 

c 

Resisting 
Moment 
Based  on 
Unit 
Stress 
of  16.000 
Lb.per 
Sq.K. 

Extreme 
Length  for 
Deflection  for 
Plastered 
Ceilings 
Limit  1-480 
Span 

For 

Uni- 
formly 
Distrib- 
uted 
Load 

For 
Cen- 

& 

For 
Uni- 
formly 
Distrib- 
uted 
Load 

For 
Cen- 
ter 
Load 

Flange  X  Stem 
X  Weight 

(In.)« 

(In.)» 

Foot- 
pounds 

Ft.  In. 

Ft. 

Flange  X  Stem 
X  Wei«ht 

(In.)« 

(In.)3 

Foot- 
pounds 

Ft.  In. 

Ft. 
In. 

T-5  x3  -13.6 

2.6 

1.18 

1,570 

6-9 

4-6 

T-3  x3  -10.1 
9.0 
7.9 

6.8 

2.3 
2.1 
1.8 
1.6 

1.10 
1.01 
0.86 
0.74 

1,470 
1,350 
1,150 
990 

6-3 

4-3 

T-5  x2i-11.0 

1.6 

0.86 

1,150 

5-6 

3-8 
4-? 
4-6 

3-10 

T-4^x3H5.9 

5.1 

2.13 

2,840 

7  2 

T-3  x2|-  7.2 
6.2 

1.1 
0.94 

0.60 
0.52 

800 
690 

5-4 

3-6 

T-4jx3  -  8.6 
-10.0 

1.8 
2.1 

0.81 
0.94 

1,080 
1,250 

6-9 

T-2fx2  -  7.4 

14 

0.75 

1,000 

4-6 

3-0 

T-4*x2£-  8.0 
9.3 

1.1 
1.2 

0.56 
0.65 

750 
870 

5^9 

T-2*x3  -  7.2 
6.2 

-1.8 
1.6 

0.87 
0.76 

1,160 
1,010 

6yX) 

4-0 

T-4  x5  -15.7 
12.3 

10.7 
8.5 

3.10 
2.43 

4,140 
3,240 

10^6 

7^0 
6^3 

T-2£x2|-  6.8 
5.9 

1.4 
1.2 

0.73 
0.60 

970 
800 

5^8 

3-9 
5^3 

T-4  x4^-14.8 
11.6 

8.0 
6.3 

2.55 

1.98 

3,400 
2,640 

9-6 

T-2^x2£-  6.5 
5.6 

1.0 
0.87 

0.59 
0.50. 

790 
670 

3-6 

T-4  x4  -13.9 
10.9 

5.7 
4.7 

2.02 
1.64 

2,690 
2,190 

8T6 

5-8 

T-2|xH-  3.0 

0.094 

0.09 

120 

3-0 

2-0 

T-4  x3  -  9.3 

2.0 

0.88 

1,170 

6-8 

4-6 
3-9 

3-0 

T-2ix2i-  5.0 
4.2 

0.66 
0.51 

0.42 
0.32 

560 
430 

4-9 

3-^0 

T-4  x2|-  8.7 
7.4 

1.2 
1.0 

0.62 
0.55 

830 
730 

5-8 

T-2  x2  -  4.4 
3.7 

0.45 
0.36 

0.33 
0.25 

440 
330 

4-0 

2-9 

T-4  x2  -  7.9 

6.7 

0.6 
0.54 

0.40 
0.34 

530 
450 

4-6 

T-2  xlj-  3.2 

0.16 

0.15 

200 

3-3 

2-2 

T-3^x4  -12.8 
10.0 

5.5 
4.3 

1.98 
1.55 

2,640 
2,070 

8-4 

5-6 

T-Hxlf-  3.2 

0.23 

0.19 

250 

3-8 

2-6 

T-Uxli-  2.6 
2.0 

0.15 
0.11 

0.14 
0.11 

190 
150 

3^3 

2-2 

T-3|x3Hl-9 
9.3 

3.7 
3.0 

1.52 
1.19 

2,030 
1,590 

7-6 

5-0 

T-Hxih  2.1 

0.08 
0.06 

0.10 
0.07 

130 
93 

2-6 

1-9 

T-3£x3  -11.0 
8.7 
7.7 

2.4 
1.9 
1.6 

1.13 
0.88 
0.72 

1,510 
1,170 
960 

6^6 

4-4 
5-4 

T-l  xl  -  1.3 

1.0 

.0.03 
0.02 

0.05 
0.03 

67 
40 

2-0 

1-4 

T-3  x4  -11.9 
10.6 
9.3 

5.2 
4.8 
4.3 

1.94 
1.78 
1.57 

2,590 
2,370 
2,100 

8-0 

T-3  x3§  11.0 
9.8 

8.6 

3.5 
3.3 

2.9 

1.49 
1.37 
1.21 

1,990 
1,830 
1.610 

7-2 

4-9 

108  STEEL  CONSTRUCTION 

This  can  be  applied  to  designing  girders  for  floor  panels.  Fig. 
86  shows  a  section  of  floor  with  several  arrangements  of  joists. 
When  the  girder  length  is  divided  by  the  joists  into  an  even  number 
of  spaces  as  2,  4,  and  6  in  (a),  (b),  and  (c),  respectively,  Fig.  86,  the 
bending  moment  on  the  girder  is  the  same  as  if  the  entire  panel  load 
were  uniformly  distributed  over  the  length  of  the  girder.  When  the 
girder  length  is  divided  by  the  joists  into  an  odd  number  of  spaces 
as  3,  5,  and  7  in  (d),  (e),  and  (f),  respectively,  the  bending  moment 
is  less  than  if  the  entire  panel  load  were  uniformly  distributed  over 
the  length  of  the  girder. 
PROBLEM 

To  prove  the  foregoing  statements,  assume  panels  20  feet  square  and  a 
load  of  100  pounds  per  square  foot.  Compute  the  bending  moments  on  the 
girder  for  all  the  cases  illustrated  in  Fig.  86. 

(a)  fr ! ^  (H^ L 


(f) 


v* - 


I   I   I   I   I   I 

Fig.  86.     Diagrams  of  Girders  Showing  Types  of  Joist  Spacing 

Shearing  Resistance.  It  has  been  stated,  p.  79,  that  the  maxi- 
mum shear  in  a  beam  section  can  be  determined  approximately  by 
assuming  that  the  entire  shear  is  resisted  by  the  web  of  the  beam. 
For  this  purpose  the  area  of  the  web  may  be  taken  as  the  total  depth 
of  the  beam  multiplied  by  the  thickness  of  the  web.  Then  the  total 
resistance  V  is  the  area  of  the  web  A  multiplied  by  the  allowable 
unit  shear  Sa  and  is  expressed  by  the  formula 


The  unit  stress  allowed  is  10,000  pounds  per  square  inch.    For 
example,  to  determine  the  shearing  resistance  of  a  12"  I  40  #: 

A=     12X0.46    =  5.52sq.  in. 
then  F=5.52X10,000  =  55,200# 

PROBLEM 

Refer  to  the  problems  given  under  bending  resistance.     Compute  the! 
-shearing  resistance  of  the  beams  and  compare  with  the  maximum  shearing  stress.. 


STEEL  CONSTRUCTION  109 

The  shearing  resistance  is  usually  much  in  excess  of  the  amount 
required.  It  need  not  be  investigated  unless  the  span  is  short  or 
unless  a  heavy  load  is  applied  near  a  support  so  that  it  produces  a 
small  bending  moment  and  high  shear.  The  values  of  the  shearing 
resistance  of  beams  are  given  in  Table  III.  By  the  use  of  this  table 
the  shearing  resistance  of  the  beam  which  has  been  selected  can  be 
compared  with  the  computed  maximum  shear  on  the  beam. 

Of  more  importance  is  the  strength  of  the  standard  end  connec- 
tions for  beams.  These  are  discussed  in  a  later  section  of  this  text. 
Their  values  are  given  in  Table  III.  In  all  cases  the  strength  of  the 
connection  is  less  than  the  shearing  strength  of  the  beam.  Hence, 
the  strength  of  the  connection  must  be  compared  with  the  maximum 
shear  on  beams.  If  the  standard  connection  is  not  strong  enough, 
a  special  one  must  be  devised  and  the  strength  of  the  web  investi- 
gated. 

Deflection.  The  deflection  of  a  beam  may  be  of  as  much 
importance  as  its  strength.  If  its  amount  is  noticeable,  it  gives 
the  impression  of  weakness.  This  is  especially  true  when  it  shows 
a  definite  change  under  the  application  and  removal  of  live  load. 
If  the  beam  deflects  unduly,  it  will  cause  cracks  in  the  supported 
material.  The  most  common  results  of  too  much  deflection  are 
cracks  in  plaster  under  the  middle  of  joist  spans  and  cracks  in  tile 
or  concrete  floors  over  the  ends  of  joists  where  they  connect  to 
girders.  This  is  shown  in  an  exaggerated  way  in  Fig.  70.  It  is  not 
uncommon  to  find  such  unsightly  cracks  in  the  tile  or  marble  floors 
of  high-grade  buildings.  It  has  been  determined  experimentally 

that  plaster  will  crack  when  the  deflection  is  — -  of  the  span,  i.  e., 

obO 

1  inch  in  30  feet;  but  a  much  lower  value  should  be  used  for  masonry 
and  for  marble  floors  and  ceilings. 

Deflection  Formulas.     Deflection  formulas  (p.  80)  are  as  follows : 

5    Wl3 
for  uniformly  distributed  load     d  =  —  -=-= 

Oo4  LJ  I 

1    W  I3 

for  load  concentrated  at  center   d  = — - 

48    LJ  I 

in  which  d  is  deflection  in  inches;  W  is  total  load;  /  is  length  in 
inches;  E  is  modulus  of  elasticity;  and  /  is  moment  of  inertia. 


110  STEEL  CONSTRUCTION 

To  illustrate  their  use,  assume  a  12"  131 2  #,  span  15  feet,  or 
180  inches,  load  u.  d.  25,000  pounds.  The  value  of  I  for  this  beam 
is  215.8.  Then 

,=    5      25,000X180X180X180 

384        30,000,000X215  8 

If  we  change  the  load  from  u.  d.  to  concentrated 
.     1      25,000X180X180X180 

48         30,000,000X215.8 

A  comparison  of  the  results  shows  that  the  deflection  is  l.G 
times  as  much  for  the  concentrated  load  as  for  the  uniformly  dis- 
tributed load.  If  both  the  above  loads  are  applied  at  the  same 
time,  the  total  deflection  is  the  sum  of  the  two  amounts  computed 
above,  i.  e., 

<*  =  0.29"-f0.47"  =  0.76" 

Formulas  are  given  in  the  handbooks  for  other  forms  of  loading, 
but  as  they  are  not  used  often  they  are  not  given  here.  Concentrated 
loads  within  the  middle  third  may  be  treated  as  if  at  the  center,  and 
if  outside  the  middle  third,  as  if  uniformly  distributed.  The  results 
from  this  approximate  method  will  be  reasonably  close  to  the  cor- 
rect values. 

Safe  Span  Length.    Based  on  a  maximum  deflection  of  — -  of 

ouO 

the  span,  and  on  a  unit  stress  of  10,000  pounds  per  square  inch,  the 
permissible  span  is  25  times  the  depth  for  a  uniformly  distributed 
load  and  15.6  times  the  depth  for  a  center  load.  These  relations  are 
correct  for  sections  symmetrical  about  the  neutral  axis,  as  I-beams 
and  channels.  They  err  on  the  safe  side  for  unsymmetrical  sections, 
as  angles  and  tees,  and  may  be  used  for  them.  These  values  should 
be  considered  the  extreme  lengths  for  beams  loaded  to  their  full 
capacity.  It  is  preferred  that  shorter  lengths  be  used  for  several 
reasons:  viz,  noticeable  deflection  is  objectionable;  the  greatest 
practicable  stiffness  is  desired;  deflection  causes  secondary  stresses 
in  the  connections. 

The  handbooks,  in  their  tables  of  "Safe  Loads  Uniformly  Dis- 
tributed for  I -beams",  limit  the  span  length  for  deflection  to  24 
times  the  depth.  The  designer  must  use  his  judgment  in  this 
matter,  giving  consideration  to  the  conditions  of  loading.  A  con- 


STEEL  CONSTRUCTION  111 

vonient  rule  for  a  u.  d.  load  is  2  feet  of  length  for  each  inch  of  depth 
(24  times  the  depth);  and  for  a  center  load  1£  feet  of  length  for 
oac-h  inch  of  depth  (16  times  the  depth).  Table  III  gives  the  max- 
imum allowable  spans  for  these  ratios,  based  on  a  unit  stress  of 
16,000  pounds  per  square  inch.  If,  however,  the  unit  stress  is  less 
than  16,000  pounds,  longer  spans  may  be  used. 

In  most  cases  the  beam  section  required  to  resist  the  bending 
moment  comes  well  within  the  limiting  length  for  deflection.  It  is 
only  when  a  long  span  has  a  relatively  light  load  'that  deflection 
must  be  considered.  This  condition  occurs  most  frequently  in  joists. 
Girders  rarely  have  excessive  deflection. 

To  illustrate  such  a  case,  assume  a  beam  of  30-foot  span  sup- 
porting a  load  of  8000  pounds  u.  d.  The  bending  moment  is  30,000 
foot-pounds,  which  requires  10"  I  25$.  The  length  of  this  beam  is 
36  times  its  depth,  therefore  the  deflection  will  be  excessive.  If  it  is 

decided  arbitrarily  to  make  the  depth  of  beam  —-of  the  span,  the  sec- 

tion required  is  15"  I  42  #.  This  beam,  if  loaded  to  full  capacity, 
would  deflect  just  to  the  allowed  limit.  But  the  resisting  moment 
of  15"  I  42$  is  79,000  foot-pounds,  more  than  twice  the  bending 
moment  computed  above,  hence  its  deflection  being  in  direct  pro- 
portion to  the  load  is  less  than  half  that  allowed.  Assume  that  the 

deflection  must  not  exceed  1  inch,  i.  e.,  ---  of  the  span.    Then  try 

«•».;       ouO    -^ 

12"  I  3H#  and  compute  the  deflection  from  the  formula 
A  w  /3  -  5      SOQQX  360X360X360 


384    El     384       30,000,000X215.8 


_„ 


As  the  computed  deflection  is  less  than  the  allowed  amount,  the 
12-inch  I-beam  is  satisfactory. 

The  problem  can  be  solved  directly  instead  of  by  trial.     Trans- 
form the  equation  to  the  form 

5       IF/3  ^5      8000  X  360  X  360  X  360 
384       Ed     384  30,000,000  X  1 

The  beam  having  a  value  7  next  higher  than  162  is  12"  I  31  \  #.  The 
handbooks  give  explanations  and  tables  for  aiding  the  solution  of 
this  problem. 


112  STEEL  CONSTRUCTION 

Attention  is  called  to  the  fact  that  usually  a  joist  receives  a 
considerable  percentage  of  its  load  (the  floor  construction)  before 
the  plastering  is  done.  It  has  already  deflected  in  proportion  to  the 
load  it  has  received.  It  is  only  the  subsequent  loading  and  the 
resulting  deflection  that  may  crack  the  plaster.  Consequently,  the 

total  deflection  might  be  much  greater  than  — -  times  the  span  and 

-«  oOU 

still  not  cause  trouble.  Nevertheless  it  is  best  to  keep  within  this 
limit 

.  The  situation  regarding  marble  or  concrete  floors  is  quite 
different.  Fig.  70  illustrates  in  an  exaggerated  way  the  joists  in 
two  panels,  connecting  to  a  cross  girder.  It  takes  but  little  deflection 
to  cause  cracks  in  the  floor  over  the  girder.  No  definite  limit  of 
deflection  has  been  determined  for  this  case.  The  writer  has  ob- 
served an  instance  where  the  deflection  appeared  to  be  less  than 

|  inch  in  a  span  of  24  feet  (about  r— r).    No  definite  suggestion  can 

oOO 

be  made  for  taking  care  of  this  difficulty  other  than  to  make  the 
joists  as  stiff  as  practicable  within  a  reasonable  cost.  Probably  this 
trouble  can  best  be  eliminated  by  the  use  of  elastic  joints  in  the 
floor  over  the  girder. 

PROBLEM 

What  I -beam  is  required  to  support  a  u.  d.  load  of  4500  pounds  on  a  span 
of  24  feet  the  permissible  deflection  being  3/2  inch? 

Lateral  Support.  If  the  top  flange  of  a  beam  is  not  supported 
laterally,  it  is  in  much  the  same  condition  as  a  column.  It  is  then 
not  capable  of  supporting  the  full  load  given  by  the  beam  formula. 
In  many  cases  where  the  lateral  support  is  not  furnished  by  the  floor 
construction,  connecting  beams,  or  otherwise,  it  can  be  supplied  by 
means  of  tie  rods  or  struts  inserted  for  that  purpose.  When  no 
such  lateral  support  can  be  provided,  the  allowable  load  must  be 
reduced. 

The  handbooks  contain  tables  which  give  the  proportion  of  the 
total  load  that  may  be  used  for  various  ratios  of  length  to  width  of 
flange.  They  permit  the  full  load  when  the  unsupported  length  is 
less  than  20  times  the  width. 

To  illustrate  the  use  of  these  tables  assume  a  12"  I  31  }#  20  feet 
long,  supported  laterally  at  the  center.  The  unsupported  length  is 


STEEL  CONSTRUCTION  113 

10  feet,  or  120  inches.    The  width  of  flange  is  5  inches.    Then  the 

120 

ratio  of  length  to  width  of  flange  is  —-  =  24.    In  the  Cambria 

o 

handbook,  the  allowable  load  is  94  per  cent  of  that  given  by  the 
beam  formula. 

In  Table  III,  the  extreme'  lengths  are  given  for  beams  without 
lateral  support  when  loaded  to  full  capacity  and  when  loaded  to 
half  capacity.  Intermediate  values  can  be  interpolated.  The 
lengths  given  are,  respectively,  20  and  60  times  the  flange  width. 
In  all  cases  beams  must  have  lateral  support  at  the  end  bearings. 

PROBLEMS 

1.  What  is  the  safe  resisting  moment  of  an  8*  I  18#  on  a  12-foot  span  when 
the  top  flange  has  no  lateral  support? 

2.  The  required  resisting  moment  of. a  beam  is  42,000  foot-pounds;  its 
unsupported  length  is  12  feet.     What  ITbeam  is  required? 


PRACTICAL  APPLICATIONS 

Panel  of  Floor  Framing.  Fig.  87  illustrates  a  typical  floor 
panel  in  a  building.  It  is  desired  to  investigate  the  various  possible 
arrangements  of  framing  for  this  panel.  Assume  that  the  dead 
load  on  the  joists  is  80  pounds  per  square  foot  including  the  weight 
of  joists  (but  not  the  weight  of  the  girders  and  their  fireproofing); 
assume  that  the  live  load  is  100  pounds  per  square  foot  on  joists, 
and  85  pounds  per  square  foot  on  girders. 

Scheme  (a).  Scheme  (a)  places  the  girders  on  the  longer  span 
and  divides  the  panel  into  4  parts.  The  joists  are  spaced  5'-4|"  c.  c. 

Area  supported  by  one  joist  16  X  5f  =  86  sq.  ft. 

dead  load  on  one  joist  86  X   80  =  6880  # 
live  load  on  one  joist  86X100  =  8600  # 

Total  load  15,480  # 

This  total  load,  15,480  pounds,  is  uniformly  distributed  on  a  span 
16  feet.  The  table  of  safe  loads  in  the  handbook  indicates  10" 
I25#. 

The  girder  carries  the  reaction  of  the  joists  on  each  side  and  the 
weight  of  itself  and  of  its  fireproofing  (assumed  at  200  pounds  per 
lineal  foot).  On  the  theory  that  the  whole  floor  will  not  be  loaded 
at  one  time,  the  live  load  on  the  girder  is  taken  at  85  pounds  per 


^—t 

*0 

/  ec 

-V  65* 

X 

,               / 

o 

1 

§ 

d 

z?a 

cs 

c. 

' 

'< 
\ 

J 

1 
* 

r    ^ 

'  1 

o 

DO 

« 



—  ^l'-6' 

, 

« 

M 

— 

} 

—  -»• 

775 

—  1- 

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1 

!                    | 

' 

.  86K8<. 
£6X<SJ 

•)'688O 
-73/0 

M 

— 

/4I90     \'4I9O     \/4/90 

^^•'^ 

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^ll3S 

ZOSO 
21/85 

.1 

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^J/<9J 

Fig.  87.     A  Panel  of  Floor  Framing 


STEEL  CONSTRUCTION  115 

square  foot.  The  length  of  span  is  taken  at  20'-6*  (allowance  being 
made  for  the  width  of  the  column).  Then  the  loads-on  the  girder 
are  as  indicated  in  the  figure  and  the  bending  moments  are 

for  u.d.  load  4100X201  -  10,500  ft.-lb. 


t  *ji    j       1+21,136X101-5 

for  concentrated  loads      (_14jl90x  5i=_76,271 

=  140,363 

Total  bending  moment  =  150,863  ft.-lb. 

From  the  table  of  resisting  moments,  p.  100,  20'  I  65$  is  indicated. 
Scheme  (b).    Scheme  (b)  places  the  girders  on  the  longer  span 
and  divides  the  panel  into  3  parts.     This  requires  for  the  joists 
12'  I  31i#;  and  for  the  girders  20'  I  65#. 

EXAMPLES  FOR  PRACTICE 

1.  Determine  the  sizes  of  joists  and  girders  required  for  scheme 
(c). 

2.  Determine  the  sizes  of  joists  and  girders  required  for  scheme 
(d).    Note  that  the  girders  are  to  be  made  of  two  I-beams.    This 
makes  the  span  of  the  joists  15'-4'. 

3.  In  scheme  (e)  the  girder  is  placed  on  the  shorter  span,  as 
shown.    Its  net  length  is  IS'-O*.    Determine  the  sizes  of  joists  and 
girders. 

4.  Determine  the  sizes  of  I-beams  required  for  scheme  (f;. 

5.  In  scheme  (g)  it  is  desired  to  make  the  joists  and  girders 
the  same  depth.    This  makes  it  necessary  to  use  two  I-beams  for  the 
girder.    What  sections  are  required? 

6.  Investigate  all  the  beams  in  the  foregoing  problems  as  to 
shear,  deflection,  and  strength  of  standard  end  connections. 

7.  Compute  the  weight  of  the  I-beams  required  for  one  panel 
for  each  of  the  above  schemes.    There  is  one  girder  for  each  panel, 
and  one  joist  for  each  division  of  the  panel,  i.  e.,  four  joists  for 
scheme  (a),  three  for  scheme  (b),  etc.    The  weights  for  scheme  (a)  are 

4  10'  I25#X15'-11'  =  1592# 
1  20"  I65#X20'-  6*  =  1333# 

8.  Which  scheme  requires  the  least  weight  of  steel? 


110  STEEL  CONSTRUCTION 

Choice  of  Scheme.  A  number  of  considerations  will  affect  the 
final  decision  as  to  the  scheme  to  be  adopted.  The  character  of 
the  floor  construction  will  limit  the  spacing  of  the  joists.  It  might 
eliminate  schemes  (b),  (c),  (d),  and  (f).  The  thickness  of  floor 
construction  may  be  important,  in  which  case  scheme  (a)  would  be 
preferred  as  to  joists  and  scheme  (g)  as  to  girders.  The  thickness 
of  floor  may  affect  it-s  cost  and  also  the  dead  load  to  be  carried  by 
joists,  girders,  and  columns^  making  the  thinner  floor  preferable  on 
this  account.  A  flat  ceiling  may  be  required  over  the  entire  area, 
in  which  case  scheme  (g)  is  applicable. 
PROBLEM 

A  space  14  feet  wide  and  100  feet  long  is  to  be  floored  over.  This  floor  is 
to  be  supported  by  joists  resting  on  brick  side  walls.  The  floor  construction  is 
such  that  the  joists  may  be  spaced  not  more  than  8  feet  c.  c.  Total  load  200 
pounds  per  square  foot.  Determine  the  most  economical  size  and  spacing  of 
joists. 

Lintels.  Flat-topped  openings  through  brick  walls  require 
lintels  to  support  the  masonry  above.  Brickwork,  after  it  has 
hardened,  will  arch  over  such  openings,  the  part  of  the  brickwork 
below  the  thrust  line  of  the  arch  being  held  in  place  by  adhesion  of 
the  mortar.  But  there  must  be  some  support  while  the  mortar  is 
green,  or  the  arch  action  may  be  destroyed  by  settlement,  making 
a  permanent  support  necessary.  The  amount  of  the  load  on  lintels 
is  uncertain.  Each  case  must  be  decided  according  to  the  condi- 
tions. 

Types  of  Construction.  In  Fig.  88  several  cases  are  illus- 
trated. 

Case  a  is  an  opening  with  a  solid  wall  above  and  at  the  sides. 
A  satisfactory  rule  in  this  case  is  to  figure  the  weight  of  brickwork 
within  the  triangle  whose  base  equals  the  width  of  opening  and  whose 
slopes  are  45  degrees. 

In  case  6  the  shaded  area  might  be  entirely  supported  on  the 
lintel  over  the  lower  opening. 

Case  c  represents  a  spandrel  wall  between  piers.  The  height  of 
the  brickwork  is  less  than  the  width  of  the  opening.  The  entire 
weight  of  the  spandrel  should  be  supported  on  the  lintel. 

In  addition  to  the  weight  of  the  brickwork,  the  lintel  may  have 
to  support  the  end  of  a  girder  as  in  case  d,  or  it  may  have  to  support 
some  floor  area  as  in  case  e. 


STEEL  CONSTRUCTION 


117 


Case/  shows  a  section  through  a  wall  in  which  the  outer  course 
of  brickwork  is  supported  by  a  lintel  and  the  remainder  by  an  arch. 

In  the  following  problems  assume  the  weight  of  brickwork  to 
be  120  pounds  per  cubic  foot.  Then  for  each  superficial  foot  of  wall 
the  weight  is  10  pounds  for  each  inch  of  thickness. 


(a) 


u 

»*5* 

LJ—  riOCK  GIRDER 

E 

»I7~ 

V                          : 
_|  j     J 

^ 

p,,I| 

(d) 

r       r       / 

/                   ; 

r—  4  '-(?"— 

] 

^>-*--J 

\ 

^ 

•    '- 
.-g-t$  —  .  —  - 

hi 

-  —  e'-o"  — 
' 
\ 

i 
3 

I 

r: 


-IP'-O"— 


Fig.  88.    Types  of  Lintels 

EXAMPLES  FOR  PRACTICE 

1.  Design  lintel  for  case  a,  span  4  feet,  wall  thickness  9  inches. 
Use  2  Ls.    The  horizontal  legs  of  the  angles  should  be  3 1  or  4  inches 
wide  to  support  the  brickwork  properly.    See  Table  II  for  formula 
for  bending  moment  for  this  condition  of  loading. 

2.  Design  the  lintel  required  for  conditions  given  for  case  b. 
Assume  that  the  channels  carry  the  entire  load. 


118 


STEEL  CONSTRUCTION 


3.  What  section  of  I-beam  is  required  for  the  lintel  in  case  c? 
Neglect  the  value  of  the  plate  on  the  bottom  of  the  beam. 

4.  In  case  d  assume  a  load  of  20,000  pounds  from  the  girder  in 
addition  to  the  weight  of  brickwork.    What  section  of  I-beam  and 
channel  are  required?    Neglect  the  value  of  the  angle. 

5.  In  case  e  assume  a  load  of  2000  pounds  per  lineal  foot  in 
addition  to  the  weight  of  the  wall.    What  section  of  I-beam  and 
channel  are  required?    The  span  is  the  same  as  for  case  c. 

6.  Determine  the  angle  required  to  support  the  face  'brick 
across  a  5-foot  opening.     (Case  /).     (The  back  is  supported  by 
brick  arches.) 

Cantilevers.    Fig.  89  snows  a  beam  projecting  beyond  the  wall 
of  a  building,  that  is,  a  cantilever  beam.    The  projection  is  6  feet 


Fl 

£!J 


—  i6-o' T^r — 

Fig.  89.     Cantilever  Construction 


from  the  face  of  the  wall.  The  load  to  be  suspended  from  the  end 
of  the  cantilever  is  10,000  pounds.  Within  the  building  the  beam 
serves  as  a  girder  on  a  span  of  16  feet.  As  such  it  supports  a  dead 
load  of  1600  pounds  per  lineal  foot  and  a  live  load  of  1700  pounds 
per  lineal  foot. 

PROBLEM 

Compute,  from  the  data  given  above,  the  reactions  and  construct  the 
moment  and  shear  diagrams  for  each  of  the  three  following  combinations  of 
loading  and  determine  the  I-beam  required: 

(1)  Dead  load  and  live  load 

(2)  Dead  load  and  suspended  load 

(3)  Dead  load,  live  load,  and  suspended  load 

Tank  Support.  Fig.  90  illustrates  the  framework  for  supporting 
a  wood _  water  tank.  The  tank  rests  on  4"X6*  wood  sub-joists 


STEEL  CONSTRUCTION 


119 


spaced  about  18  inches  center  to  center.  These- in  turn  rest  on 
steel  joists.  The  load  on  the  steel  joists  may  be  considered  as 
uniformly  distributed. 


Fig.  00.     Plan  and  Elevation  of  Tank  Support 

To  compute  the  volume  and  weight,  use  the  outside  dimensions 
of  the  tank.     (Assume  the  weight  of  water  to  be  62.5  pounds  per 
cubic  foot.)    This  will  give  some  excess  which  will  be  sufficient  to 
cover  the  weight  of  the  steel  beams.    On  this  basis 
3.1416X13X13, 


volume 


-Xl6  =  2125cu.  ft. 


weight  =2125X62.5  =  132,800# 


120 


STEEL  CONSTRUCTION 


This  can  be  used  as  a  check  on  the  sum  of  the  partial  loads.  The 
load  per  square  foot  for  16  feet  of  water  is  16X62.5  or  1000 
pounds. 

PROBLEMS 

1.  Lay  out  an  assumed  plan  of  the  framework  and  the  outline  of  the  tank 
accurately  to  scale.     Determine  the  area  supported  by  each  beam  by  measure- 
ments from  the  scale  drawings  as  indicated  by  the  shaded  areas  in  the  figure. 

2.  Compute  the  bending  moment  and  shear  for  the  several  joists  and  the 
girders,  and  select  the  required  I-beams.     Check  for  strength  of  end  connections. 

DETAILS  OF  CONSTRUCTION 

Connection  of  Beams  to  Beams.  When  one  beam  bears  on  top 
of  another,  the  only  connection  required  is  rivets  or  bolts  through 
the  flange,  as  shown  in  Fig.  Ql.  No  stress  is  transmitted  by  these 


Fig.  91.     Riveted  Con- 
nection of  Beam  to 
Beam 


Fig.  92.    Beam  Connections  by  Means  of  Sheet 
Steel  Clips 


rivets  or  bolts.  They  serve  simply  to  hold  the  beams  in  position. 
Steel  clips  are  sometimes  used  for  this  purpose,  Fig.  92,  but  as  they 
are  not  positive  in  holding  the  beams  in  position  they  are  not  as 
good,  especially  when  lateral  support  is  required.  When  this  is  not 
important,  the  clips  can  be  used  and  may  effect  a  saving  in  cost. 
These  clips  are  most  useful  for  attaching  tees  and  angles  to  beams  in 
ceiling  and  roof  construction. 

Angle  Connections.  The  most  common  method  of  connecting 
one  beam  to  another  is  by  means  of  angles  riveted  to  the  web.  There 
are  several  sets  of  standard  connections,  various  concerns  having 
their  own  standards.  Those  of  the  American  Bridge  Company  are 


STEEL  CONSTRUCTION 


121 


given  in  Fig.  93.*  The  values  given  in  Table  III  are  based 
on  these.  The  two-angle  connection  is  generally  used,  but  when 
beams  are  used  in  pairs  or  iwhen  for  any  reason  the  two-angle  con- 


TWO  ANGLE:  CONNECTIONS 


OfiC  ANGLE   CONNECTIONS 


24" 


WT.  JO* 


I   ANGLE    6"X6"Xi6Xl'-5?" 


WT.  25 


^  ANGLES  4 


15" 


I?* 


2  AH6L CS     6'X  4"X 


'WT. 


2  AHGLTS     6"X  4" X R  X  5" 


I   ANGLE      6"*  6'Xfc'x  5" 


3f*4        ff( 

5"&  6"   ^  ANGLES  6"x 
J"&  4'   ^  ANGLES  6x 


f^"&  6"WT.  5* 
'&  4'WT.  4 


3"&  4"    I  ANGLE  6"* 6"X £ X  ^'i 


Fig.  93.     Beam  Connection  Angles 
Used  by  American  Bridge  Company 

nection  cannot  be  used,  the  one-angle  connection  is   used.    The 
rivets  used  in  the  standard  connections  are  J  inch  in  diameter. 

"Subsequently  a  different  set  of  standarda  has  been  adopted.     See  Carnegie  Pocket  Com- 
panion, 1913  edition. 


122 


STEEL  CONSTRUCTION 


The  strength  of  the  two-angle  connection  may  be  limited  by 

(1)  Shop  rivets  in  double  shear 

(2)  Field  rivets  in  single  shear 

(3)  Shop  rivets  in  bearing  in  web  of  joist 

(4)  Field  rivets  in  bearing  in  web  of  girder 

For  example,  take  the  connection  for  a  15"  I  42$: 

(1)  6  shop  rivets  in  double  shear 

6X10,300  =61,800# 

(2)  8  field  rivets  in  single  shear 

8X  4420  =  35,360  # 

(3)  6  shop  rivets  in  bearing  in  web  of  joist 

6  X.  41 X.  75  X  25,000  =  46,125  # 

(4)  8  field  rivets  in  web  of  girder;  the  thickness  of  the  web  is  not 
given.     It  must  be  at  least  0.30  inch  for  a  connection  on  one 
side  only,   or  of   twice  this  thickness  if  an   equal    connectioh 
is  on  the  opposite  side,  in 

order  to  have  the  same 
strength  as  the  field  rivets 
in  shear. 


Jif 


COPE    TO 
I8"l  35* 


Fig.  94.     Plate  Riveted  to  Web  of 

I-Beam  to  give  Additional 

Bearing 


/<?/ 


COPE  TO  # 
12"!  3/j 


Fig.  95.     Diagrams  of  Coped  Beams 


The  shearing  strength  of  this  connection,  35,360  pounds,  corre- 
sponds to  the  maximum  safe  u.  d.  load  on  a  span  of  about  9  feet. 
It  is  less  than  the  shearing  strength  of  the  web  of  the  beam.  It 
rarely  happens  that  the  strength  of  the  connection  is  less  than 
required,  and  occurs  only  when  the  beam  is  short  and  heavily  loaded 
or  when  a  heavy  load  is  applied  near  the  end.  Lack  of  bearing  in 
the  web  of  the  girder  is  more  likely  to  occur,  but  this  is  not  fre^- 


«"!  > 


)  ( 

)  ( 

)  ( 

)  ( 


r 


iff 


00 
O  O 


O  O 

O 
O  O 


\ 

i 

oo  i 

I 

o  i 

• 

oo  i 

i 

\                     f7=3 

^> 

o  o 

)  O  O 
Tt~4^ 


Fig.  96.    Types  of  Beam  Connections 


124 


STEEL  CONSTRUCTION 


quent.  If  it  does  happen,  however,  angles  with  6-inch  legs  may  be 
used  to  provide  space  for  more  rivets,  or  a  reinforcing  plate  may 
be  riveted  to  the  web  of  the  girder,  Fig.  94. 

Special  Connections.  When  beams  on  the  two  sides  of  a  girder 
do  not  come  opposite  or  are  of  different  sizes  so  that  the  standard 
connections  do  not  match,  it  is  necessary  to  devise  a  special  connec- 
tion. If  a  beam  is  flush  on  the  top  or  on  the  bottom  with  the  one  to 
which  it  connects,  the  flange  must  be  coped,  Fig.  95.  A  number  of 
special  connections  are  shown  in  Fig.  96  and  need  no  explanation. 

Connections  of  Beams  to  Columns.  A  beam  may  connect  to  a 
column  by  means  of  a  seat  or  by  means  of  angles  on  the  web.  The 

great  variety  of  conditions  that 
may  be  encountered  make  it  im- 

k  I  ^ practicable  to  have  standards  for 

==\  TsfaTB  these  connections,  though  the 
work  of  each  shop  is  standard- 
ized to  some  extent. 

Seat  Connections.  The  seat 
connection  is  shown  in  Fig.  97. 
This  seat  or  bracket  is  made  up 
of  a  shelf  angle,  one  or  two 
stiffener  angles,  and  a  filler  plate. 
The  load  is  transmitted  by  the 
rivets,  acting  in  single  shear, 
which  connect  the  bracket  to  the 
column.  The  number  of  rivets 
used  is  proportioned  to  the  actual  load  instead  of  being  standardized 
for  the  size  of  the  beam.  The  stiffener  angles  support  the  horizontal 
leg  of  the  shelf  angle  and  carry  the  load  to  the  lower  rivets  of  the 
connection. 

Shelf  angles  are  6  inches,  7  inches,  or  8  inches  vertical  and  4 
inches  or  6  inches  horizontal,  having  a  thickness  of  ft  inch  to  f  inch, 
depending  on  the  size  of  beam  and  the  load.  The  leg  of  the  stiffener 
angle  parallel  to  the  web  of  the  beam  is  usually  \  inch  or  1  inch  less 
than  the  horizontal  leg  of  the  shelf.  The  leg  against  the  column  is 
governed  by  the  gage  line  of  the  rivets  in  the  column.  The  filler  is 
the  same  thickness  as  the  shelf  angle.  An  angle  connecting  the  top 
flange  of  the  beam  to  the  column  is  generally  used.  It  is  not  counted 


^ 

4 

-o 

<>• 

-o 

g 

•<> 
-(> 

Fig.  97.    Seated  Connection  of  Beam  tor  Column 


STEEL  CONSTRUCTION 


125 


as  carrying  any  of  the  load,  but  serves  to  hold  the  top  of  the  beam 
in  position  and  stiffens  the  connection.  The  rivets  connecting  the 
bottom  flange  of  the  beam  to  the  shelf  serve  only  to  hold  the  mem- 


>-^ 


Fig.  98.     Types  of  Scat  Connections 


bers  together  and  make  a  stiff  connection.     Usually  there  are  only* 
two  rivets  in  each  flange  but  sometimes  larger  angles  and  more 


126 


STEEL  CONSTRUCTION 


rivets  are  used  to  develop  resistance  to  wind  stresses.    Fig.  98  gives 
.a.  number  of  examples  of  seat  connections. 
The  advantages  of  the  seat  connection  are 

^•1)  All  shop  riveting  is  on  the  column  which  is  a  riveted 
member.  No  shop  riveting  is  required  on  the  beam 
which  thus  needs  only  to  be  punched 

(2)  The  seat  is  a  convenience  in  erecting 

(3)  The  rivets  which  carry  shear  are  shop  driven 

(4)  The  number  of  field  rivets  is  small 

Web  Connections.    The  web  connection  is  made  by  means  of 
two  angles,  Fig.  99.     The  legs  parallel  to  the  beam  rivet  to  the 

wreb  and  the  outstanding  legs  to 
the  columns.  The  connection  to 
the  web  of  the  beam  is  governed 
by  the  same  conditions  as  the 
standard  beam  connection.  The 
length  of  the  outstanding  leg  is 
governed  by  the  gage  lines  of  the 
rivets  in  the  column  or  the  space 
available  for  them.  Usually  the 
angles  are  shop  riveted  to  the 
beam  and  field  riveted  to  the 

column.  If  the  angles  were  shop  riveted  to  the  column,  it  would  be 
difficult  or  impossible  to  erect  the  beam.  However,  one  angle  may 
be  shop  riveted  to  the  column  and  the  other  furnished  loose.  In  this 
case  the  number  of  field  rivets  generally  will  be  the  same  as  if  the 


Fig.  99.     Web  ConncctioB  of  Beam  to  Column 


) 


y  f 


L/HE  Of   FIREPROOFIING 


Fig.  100.     Diagrams  Showing  Disadvantage  of  Seat  Connection  for  Fireproofing 

angles  were  shop  riveted  to  the  beam,  but  the  shop  riveting  on  the 
beam  will  be  eliminated,  which  is  an  advantage.     When  this  connec- 


STEEL  CONSTRUCTION  127 

tion   is   used,  a   small   seat  angle  is  provided   for  convenience  in 
erecting. 

The  advantage  of  the  web  connection  is  the  compactness  of 
the  parts,  keeping  within  the  limits  of  the  fireproofing  and  plaster, 
whereas  the  seat  connection  may  necessitate  special  architectural 
treatment  to  fireproof  it  or  conceal  it,  Fig.  100. 

Combination  Connections.  A  combination  of  web  and  seat 
connections  may  be  used  to  meet  special  conditions.  For  example, 
the  load  may  be  too  great  for  a  web  connection,  and  at  the  same 
time  a  seat  connection  may  be  objectionable.  The  combination 
will  reduce  the  seat  connection  to  a  minimum,  perhaps  eliminating 
the  stiffener  angles.  Another  case  is  where  top  and  bottom  angles 
are  required  for  wind  bracing  but  stiffener  angles  are  not  permitted ; 
there  the  combination  can  be  used. 

The  objection  to  the  combination  is  that  there  are  two  groups 
of  rivets  for  supporting  the  load.  If  the  connection  is  not  accurately 
made,  the  entire  load  may  be  carried  by  one  group  of  rivets.  A 
number  of  miscellaneous  connections  are  illustrated  later  in  the  text 
under  column  details. 

Separators.    When  beams  are  used  in  pairs  or  groups,  some 
connection  is  usually  made  between  them  at  short  intervals.    The 
connecting  piece  is  called  a  "sep- 
arator".    If  the  purpose  to  be 
served  is  merely  to  tie  the  beams 
together  and  keep  them  properly 
spaced,  the  gas-pipe  separator  is 
used,  Fig.  101.    This  consists  of 
a  piece  of  gas  pipe  with  a  bolt 
running  through  it.    This  form 

Fig.  101.     Gas-Pipe  Separators 

is  used  in  lintels  and  in  grillage 

beams.     For  beams  6  inches  or  less  in  depth,  one  separator  and 

bolt  may  be  used;  for  greater  depth,  two  should  be  used. 

The  separator  most  commonly  used  is  made  of  cast  iron,  Fig. 
102.  It  not  only  serves  as  a  spacer  but  it  stiffens  the  webs  of  the 
beams  and,  to  a  limited  extent,  transmits  the  load  from  one  beam 
to  the  other  in  case  one  is  loaded  more  heavily.  It  seldom  fits 
exactly  to  the  beam  so  it  cannot  be  relied  upon  to  transmit  much 
load.  One  bolt  is  used  for  beams  less  than  12  inches  deep  and  two 


128 


STEEL  CONSTRUCTION 


bolts  for  12-inch  and  deeper  beams.  The  dimensions  and  weights 
of  separators  and  the  bolts  for  them  are  given  in  the  handbooks. 
They  can  be  made  for  any  spacing  of  beams  and  special  shapes  can 


I 


Fig.  103.    Special  Type  of  Cast-Iron 
Separators 


Fig.  102.     Cast-iron  Separators 


be  made  for  beams  of  different  sizes, 
Fig.  103. 

The  individual  beams  of  a  pair 
or  group  should  be  designed  for  the 
actual  loads  which  they  carry,  if  it  is 
practicable  to  do  so.  If  it  is  necessary 
to  transfer  some  load  from  one  to  the 
other,  a  steel  separator  or  diaphragm 
should  be  used.  This  may  be  made  of  a 


91 

ioi 

o! 


CM 
OJ 
o: 


Fig.  104.     Steel  Separator  or  Diaphragm 


plate  and  four  angles  or  of  a  short  piece  of  I-beam  or  channel,  Fig. 
104.  If  the  beams  are  set  close  together,  the  holes  must  be  reamed 
and  turned  bolts  must  be  used  in  order  to  get  an  efficient  con- 


STEEL  CONSTRUCTION 


129 


nection.     If  the  beams  are  set  with  four  inches  or  more  clearance 
between  the  flanges,  the  separator  can  be  riveted  to  the  beams. 

Specifications  usually  require  that  separators  be  spaced  not 
further  than  five  feet  apart.  They  should  be  placed  at  points  of 
concentrated  loads  and  over  bearings. 


Fig.  105.     Layout  Showing  Tie-Rod  Connections  Between  Joists 

Tie=Rods.  A  common  form  of  fireproof  floor*  construction  is 
the  hollow  tile  arch  between  steel  joists  spaced  from  5  feet  to  7  feet 
apart.  The  arch  exerts  a  thrust  sidewise  on  the  beams  and  would 
spread  the  beams  apart  and  cause  the  arch  to  fall,  if  they  were  not 
tied  together.  Rods  f  inch  in  diameter  are  used  for  these  ties. 
They  are  spaced  about  6  feet  apart  and  placed  3  or  4  inches  above 
the  bottom  of  the  beams.  After  the  arch  construction  is  in  place, 
the  thrusts  on  the  two  sides  of  a  beam  would  balance  if  equally 


5EGMENTAL     TERRA  COTTA     ARCH  COHSTRUCTIOn 
Fig.  106.     Tie- Rod  Connections  for  Segmental  Arches 

loaded  so  that  under  these  conditions  the  rods  would  be  needed 
only  in  the  outside  panels.     However,  they  are  needed  in  all  panels 


130 


STEEL  CONSTRUCTION 


during  construction  and  as  the  loads  on  the  several  panels  may  be 
unequal,  they  are  retained  throughout  the  floor  construction,  Fig.  105. 
If  long  span  segmental  arches  are  used,  the  thrust  is  much 
greater.  Its  amount  must  be  computed  and  the  tie-rods  propor- 
tioned for  the  actual  stress,  Fig.  106. 

Bearings.  :.  Dimensions  of  Bearing  Plates.  Under  Unit 
Stresses  ate  given  the  safe  bearing  values  on  masonry.  The  end  of 
a  beam  testing  on  masonry'  usually  does  not  have  sufficient  bearing 
area,  and  a  bearing  plate  is  required.  The  area  of  the  plate  is 
determined  by  dividing  the  load  (the  end  reaction  of  the  beam)  by 
the  allowed  unit  pressure  on  the  masonry.  For  example,  assume  a 
15"  I  42$  bearing  on  a  wall  of  hard  brick  in 
cement  mortar,  the  reaction  at  the  bearing  being 
18,000  pounds.  The  allowable  pressure  is  200 
pounds  per  square  inch.  Then  the  required 
18,000 


r 

03 

L 


area  of  the  plate  is 


200 


or  90  square  inches. 


Fig.  107.   Diagram  Show 
ing  Bearing  Plata./ 


A  plate S"X12"  or  one  1.0"XlO"  would  be  used. 

The  required  thickness  of  the  bearing  plate 
depends  on  the  pressure  per  square  inch  on  the 
masonry  and  the  projection  of  the  plate  beyond 
the  flange  of  the  beam.  ,(  This  projecting  portion 
of  the  plate  acts  as  an  inverted  cantilever  with  a 
u.  d.  load.  Thus  in  Fig.  107  the  beam  is  a  15" 
I  42  #,  the  plate  8"X  12".  The  projection  of  the 
plate  is  3^  inches  and  the  upward  pressure  per 
square  inch  is  200  pounds.  To  determine  the 
thickness,  assume  a  strip  1  inch  wide;  then  there 
is  a  cantilever  3|  inches  long  with  a  load  of  200  pounds  per  inch. 
^  The  bending  moment  is 

>  3.25X200X— 0— =  105Gin.-lb. 

/ 

From  the  bending  moment  the  required  section  modulus  —  can  be 

c 

obtained  by  the  formula  given  on  p. -98;  and  from  it  the  thickness  t 
of  the  plate  can  be  obtained  by  the  formula  given  on  p.- 37,  thus 

I  =  M  =  J  050 

c       X       10,000  ~'Ub 


STEEL  CONSTRUCTION 


131 


From  the  section  modulus  the  thickness  t  can  be  computed  by 
the  reverse  of  the  method  previously  given  for  computing  /,  thus 

1  t 

I =  —  bta        o  =  1         c  —  — 

19  9 

i  —i  A 

_L  =  -L  ^  =  1*2 

c       12  _*_       6 
2 

*2  =  6X-  =  6X.066=.396 
c 

*  =  V7396  =  0.63",  or  |"  thick 

The  square  root  can  be  figured  by  the  usual  rules  but  can  be 
obtained  more  easily  from  tables  in  the  handbook. 

Graphical  Diagram  for  Designing  Bearing  Plates.    Fig.  108  is  a 
graphical  diagram  for  designing  bearing  plates.    Along  the  left  side 


?;n 


m 


Tzwr 

y&rS 


THICKNE 35     Of  PLA  TE  Ifi  IrtCHES 
(Mult  iplu  by  Z}  for  Caar  Jron) 

Fig.  108.     Diagram  for  Determining  Thickness  of  Steel  Bearing  Plates 

is  given  the  projection  of  the  plate  in  inches;  along  the  bottom  is 
the"  thickness  in  inches;  the  diagonal  lines  represent  the  several 
allowable  pressures  for  different  classes  of  masonry.  Having  com- 
puted the  size  of  plate  needed  for  bearing,  find  the  amount  of  its 
projection  beyond  the  flange  of  the  beam.  Enter  the  diagram  at 
the  left  on  the  horizontal  line  corresponding  to  the  projection;  trace 


132 


STEEL  CONSTRUCTION 


to  the  right  to  the  diagonal  line  representing  the  pressure;  then 
vertically  downward  to  the  bottom  of  the  diagram  and  read  the 
thickness.  For  example,  assume  a  projection  of  3J  inches  and  an 
allowable  bearing  of  200  pounds  per  square  inch ;  the  required  thick- 
ness is  |  inch. 

Standard  Bearing  Plates.  In  the  handbooks  are  given  standard 
bearing  plates  for  the  various  sizes  of  beams.  One  size  of  plate  is 

given  for  each  size  of  beam,  hence 
these  standard  plates  are  designed 
for  the  heaviest  loads  likely  to 
be  carried  by  the  heaviest  beam 
section  and,  consequently,  are 
larger  than  needed  for  most  cases. 
In  the  example  given  above,  the 
Cambria  standard  plate  is  12"  X 
15"  Xf".  It  is  larger  than  re- 
quired, thus  showing  that  it  is 
economical  to  design  the  plates 
for  the  actual  loads  and  the 
allowable  bearing  pressures.  In 
this  same  example,  if  the  bearing 
is  on  concrete  at  400  pounds  per 
square  inch,  no  plate  is  required 
as  the  beam  flange  alone  gives 
the  necessary  area. 

Penetration  into  Wall.  The 
penetration  of  beams  into  the 
wall,  if  the  thickness  of  wall 
permits,  should  be  not  less  than 

Fig.  109.     I-Beams  Used  For  Bearing  the  f  ollowing : 

for    3-inch,    4-inch,    5-inch,  and    6-inch  beams  and  channels  6  inches 

for                                7-inch,  and    8-inch  beams  and  channels  8  inches 

for                                9-inch,  and  10-inch  beams  and  channels  10  inches 

for                               12-inch,  and  15-inch  beams  and  channels  12  inches 

for  18-inch,  20-inch,  21-inch,  and  24-inch  beams  and  channels  15  inches 

When  the  thickness  of  the  wall  does  not  permit  the  penetration 
recommended  above,  the  allowable  bearing  stress  should  be  reduced. 
The  reduction  should  be  50  per  cent  for  heavy  beams  on  an  8-inch 


STEEL  CONSTRUCTION 


133 


bearing.  A  penetration  less  than  S  inches  should  never  be  used  for 
beams  8  inches  or  more  in.  depth.  Because  all  beams  deflect  under 
load  their  bearing  plates  should  be  set  with  a  slight  slope  downward 
toward  the  face  of  the  wall,  J  inch  per  foot  being  a  satisfactory  slope. 
This  prevents  the  whole  load  from  being  concentrated  on  the  front 
edge  of  the  plate. 

Plates  thicker  than  1   inch  are  difficult  to  get.    When  this 
thickness  is  not  enough  for  the  projection  desired,  one  or  more 


Fig.  110.     Anchors  for  Beams 


I-beams  or  channels  should  be  used  for  the  bearing,  Fig.  109.    These 
are  designed  as  inverted  cantilevers  in  the  regular  way. 

Cast-Iron  Plates.  The  foregoing  discussion  relates  to  steel 
plates.  Cast-iron  plates  may  be  used.  The  method  of  designing 
them  is  the  same  as  for  steel  plates,  except  that  the  allowable  fiber 
stress  is  3000  pounds  per  square  inch.  On  account  of  this  differ- 
ence in. the  allowable  stress,  the  thickness  of  the  cast-iron  plate  is 
2|  times  the  thickness  of  the  steel  plate.  The  diagram,  Fig.  108, 
may  be  used  for  cast  iron  by  first  determining  the  thickness  for 


134 


STEEL  CONSTRUCTION 


steel  and  multiplying  the  result  by  2}.  In  most  localities  the  cast 
iron  costs  more  than  steel  on  account  of  the  additional  weight. 

Anchors.  Beams  bearing  on  masonry  are  usually  anchored  to 
it  to  give  greater  stability  to  the  structure  as  a  whole.  Fig.  110 
shows  the  common  forms  of  anchors  used  for  this  purpose.  The 
bent  rod  a  is  the  cheapest.  The  angle  lugs  b  are  the  most  efficient. 
The  other  forms  are  used  for  the  special  conditions  indicated.  The 
thickness  of  metal  used  is  arbitrary,  usually  J  inch  for  rods  and 
f  inch  for  angles  and  plates. 

Miscellaneous  Details.  Almost  every  structure  presents  some 
conditions  requiring  special  details  of  the  beams.  The  relative 
position  of  the  steel  members  may  require  a  special  form  of  con- 
nection, or  the  other  materials  of  construction  may  necessitate 
special  details  for  their  support.  A  number  of  such  details  will  be 
shown  in  connection  with  the  practical  designs  later  in  this  text. 

RIVETED    GIRDERS 

Definition.  The  term  "riveted  girder"  is  here  used  to  apply 
to  all  riveted  beams,  i.  e.,  beams  made  of  two  or  more  steel  sections 


r\  r\... 


(<*) 


(c) 


Fig.  111.     Types  of  Riveted  Girders 

riveted  together.    The  most  common  forms  of  riveted  girders  are 
illustrated  in  Fig.  Ill  as  follows: 

(a)  I-beam  with  flange  plates  (c)     Plate  box  girder 

(b)  Plate  girder  (d)    Beam  box  girder 


STEEL  CONSTRUCTION 


135 


THEORY  OF  DESIGN 

Determination  of  Resisting  Moment.  All  that  was  stated  under 
Review  of  Theory  of  Beam  Design  applies  as  well  to  riveted 
girders  as  to  rolled  beams,  provided  the  sections  are  so  riveted 
together  that  they  act  as  a  single  piece.  However,  there  are  two 
methods  of  determining  the  resisting  moment,  viz,  by  moment  of 
inertia  and  by  chord  stress,  Fig.  112. 

Moment  of  Inertia  Method.  The  procedure  for  determining 
the  resisting  moment  of  a  beam,  or  girder,  by  means  of  the  moment 
of  inertia  has  been  fully  explained.  The  value  of  /  for  the  single 


Fig.  112.     Diagram  of  Bending  Stresses  in  a  Riveted  Girder,     (a)    Moment  of  Inertia  Method: 
-(b)     Chord  Method 

rolled  section,  such  as  the  I-beam,  is  taken  from  the  tables  in  the 
handbook,  but  for  the  riveted  girder  it  must  be  computed. 

Chord  Stress  Method.  The  second  method  of  designing  riveted 
girders  assumes  that  the  tensile  stresses  are  resisted  by  the  tendon 
flange  and  the  compressive  stresses  by  the  compression  flange.  It 
is  assumed  that  the  stress  is  uniformly  distributed  over  the  entire  area, 
of  the  flange.  Then  the  moment  of  resistance  is  the  same  as  if  the 
whole  stress  were  acting  at  the  center  of  gravity  of  the  flange  area. 

The  resisting  moment  determined  from  the  moment  of  inertia  is 

n/ 


The  resisting  moment  by  the  chord  method  is  as  follows :  In  Fig. 
112,  t  and  c  represent,  respectively,  the  total  tension  and  total 
compression  values  of  the  flanges,  applied  at  the  centers  of  gravity 
of  the  flange  sections.  The  distance  d  between  them  is  called  the 
"effective  depth  of  the  girder".  In  order  to  have  equilibrium,  /  must 
equal  c.  Each  must  equal  the  area  A  of  the  flange  multiplied  by 


136  STEEL  CONSTRUCTION 

the  unit  stress  S.    Then  t  —  c  ==  A  X  S,  and  the  resisting  moment  is 


Having  determined  the  bending  moment  in  inch-pounds  from  the 
loads  on  a  girder,  the  procedure  by  the  chord  method  is  as  follows  : 

Assume  the  total  depth  of  girder  and  from  this  approximate  the 
effective  depth  d  in  inches.  This  can  be  taken  at  2  to  4  inches  less 
than  the  total  depth,  depending  on  the  size  of  flange  angles.  By 
dividing  the  bending  moment  M  by  the  effective  depth  d,  the  flange 
stress  t  or  c  is  obtained;  and  dividing  the  flange  stress  by  the 
average  unit  stress,  say  14,500  pounds  per  square  inch,  the  result  is 
the  net  area  in  square  inches  required  for  the  flange.  The  sections 
required  to  make  up  this  net  area  can  then  be  determined. 

The  foregoing  computations  are  expressed  by  the  formula 

A-& 

~Sd 

The  average  value  of  the  unit  stress  to  be  used  is  proportioned  from 
the  extreme  fiber  stress,  16,000  pounds  per  square  inch.  Thus  if 
the  effective  depth  is  yV  of  the  extreme  depth,  the  average  unit 
stress  to  be  used  is  yV  of  16,000,  or  14,400  pounds  per  square  inch. 

The  result  of  the  first  trial  is  only  approximate.  From  the 
section  thus  determined  the  value  of  d  can  be  computed  and  the 
above  operations  repeated.  This  result,  which  is  also  approximate 
if  any  change  is  made  in  the  section,  is  usually  accurate  enough  to 
be  accepted  as  final.  Most  specifications  permit  J  of  the  v/eb  to 
be  counted  in  each  flange  section. 

Illustrative  Example.  Assume  M  equals  420,000  foot-pounds; 
total  depth  of  girder  36  inches;  approximate  value  of  d  equals  33 
inches.  To  find  the  required  section 

.¥  =  420,000X12  =  5,040,000  in.-lb. 
A      5,040,000 


{J  web  36"  XTY'  =   1.41sq.  in. 

2Ls6"X3|"Xf"  =  11.10 
less  1  rivet  hole=  1.10   =10.00 
^  =  11.41sq.  in. 

As  the  area  of  the  chosen  section  is  greater  than  the  calculated 
value,  it  is  satisfactory. 


STEEL  CONSTRUCTION 


137 


PROBLEM 

Fig.  113  illustrates  1he  plate  girder  described  in  the  above  example.  Com- 
pute the  correct  value  of  d.  (Note:  No.  account  is  taken  of  the  part  of  web 
plate  which  is  counted  as  flange  section,  in  computing  the  position  of  the  c.  g. 
of  the  flange.  Also  no  account  is  taken  of  the  rivet  H  ,.  .SH 

holes  in  the  web.)     Compute  the  net  flange  area  re- 
quired and,  if  necessary,  correct  the  size  of  angles. 

The  two  methods  of  designing  lead  to 
about  the  same  results.  No  further  consid- 
eration will  be  given  to  the  chord  method, 
as  the  moment  of  inertia  method  is  preferred. 

Calculation  of  Load  Effects.  The  bend- 
ing moments  and  shears  are  computed  in 
just  the  same  manner  for  girders  as  for 
beams.  However,  in  making  a  complete 
design  of  a  riveted  girder  the  bending  moment 
is  required  for  all  points  along  the  girder 
for  computing  rivet  spacing  and  for  deter- 
mining the  length  of  cover  plates,  if  they  are 
used.  Consequently  the  moment  diagram  is 
needed  in  most  cases.  (It  can  be  constructed  Fig.  113.  Section  and  Details 

.  .  .11.  ,1  A-  of  Plate  Girder 

by  the  methods  given  in  the  sections  on 

Bending  Moments  and  Moment  Diagrams  in  "Strength  of  Mate- 
rials".) 

DESIGN  OF  PLATE  GIRDER 

Having  computed  the  bending  moments  and  shears  and  con- 
structed the  diagrams  for  them,  the  steps  in  the  design  are: 

Determine  allowable  depth  \y 
Compute  thickness  of  web  y. 
Compute  required  moment  of  inertia 
Compute  flange  section  which  will  give  required  mo- 
ment of  inertia 

Determine  length  of  flange  plates 
Design  stiffeners 
Design  end  connection 
Compute  spacing  of  rivets  for  flanges 

For  illustrating  the  operations,  assume  a  plate  girder  as  shown 
in  Fig.  114.  The  span  is  45'-0";  load  4000  pounds  per  lineal  foot 
equals  total  load  of  180,000  pounds;  end  shear  90,000  pounds; 


138 


STEEL  CONSTRUCTION 


maximum  bending  moment  12,150,000  inch-pounds.    The  shear  and 
moment  diagrams  are  given. 

Depth.  Economy.  For  any  set  of  conditions  governing  the 
design  of  a  plate  girder  there  is  a  depth  which  gives  the  greatest 
economy  of  metal.  But  there  are  so  many  conditions  entering  into 
the  problem  that  no  simple  formula  can  be  given  for  computing  it. 


/8O.OOO    U.D, 


1 

S-o  , 

t4-C\ 

s'-°"> 

,4-0 

4-0 

4-0 

4-O 

4-0 

4-0 

4-6 

'90,000* 


MOMENT  PI  A  GRAM 
Fig.  114.    Plate  Girder  Design 


The  effects  of  some  of  these  conditions  can  be  stated  in  general 

terms  as  follows: 

The  greater  the  shear  the  greater  the  depth  required 

The  greater  the  bending  moment  the  greater  the  depth  required 

The  longer  the  span  the  greater  the  depth  required 

The  thicker  the  web  plate  the  less  the  depth 

For  lateral  stiffness  shallow  depth  is  better 

The  smaller  the  deflection  allowed  the  greater  the  depth  needed 


STEEL  CONSTRUCTION  139 

If  it  is  desired  to  determine  the  most  economical  depth  for  a 
given  case,  several  depths  must  be  assumed,  the  designs  made,  and 
the  cross  sections  or  weights  computed.  A  few  trials  will  lead  to 
the  desired  result. 

The  depth  of  the  girder  may  be  as  small  as  -fa  of  the  span  and 
may  be  as  great  as  J  the  span,  but  the  usual  range  is  A  to  J.  In 
the  absence  of  any  governing  feature  J  of  the  span  may  be  assumed 
as  a  suitable  depth. 

Other  Consideration*.  Usually  other  considerations  than  econ- 
omy will  determine  the  depth.  In  building  construction  it  is  gener- 
ally desirable  to  make  the  girders  as  shallow  as  practicable,  then  the 
depth  may  be  governed  by  deflection,  by  practicable  thickness  of 
web  or  section  of  flanges,  or  by  details  of  connections.  The  final 
result  must  be  determined  by  trial  designs. 

In  the  example,  Fig.  114,  assume  the  depth  of  web  plate  to  be 
48  inches.  On  account  of  the  fact  that  the  edges  of  the  plate  will 
not  be  exactly  straight  (unless  they  have  been  planed),  it  is  custom- 
ary to  set  the  flange  angles  J  inch  beyond  the  edge  of  the  plate, 
making  the  depth  in  this  case  48J  inches  back  to  back  of  angles. 

Thickness  of  Web.  In  building  work,  ^  inch  is  a  suitable 
thickness  to  adopt  as  the  minimum.  For  exceptional  cases  when 
the  loads  are  light  J  inch  may  be  used.  Under  Unit  Stresses, 
p.  51,  the  allowable  shear  on  girder  webs  is  given,  i.  e.,  10,000 
pounds  per  square  inch.  This  is  the  .average  shear  on  the  net 
cross  section  of  the  wet).  In  the  example,  Fig.  114,  the  maximum 

90  000 
shear  is  90,000  pounds;  then  the  net  area  of  the  web  must  be      '^^ 

.LUjUUU 

or  9.0  square  inches.  The  depth  of  the  web  is  48  inches,  from  which 
must  be  deducted  2  rivet  holes  J  inch  in  diameter,  making  the  net 
depth  46J  inches.  The  thickness  required  to  give  the  net  cross 

9  0 
section-is      '      or  0.19  inches.    Hence  a  plate  0.19  inch  thick  fulfills 

4u .  ^O 

the  requirements  for  shear  on  the  web.    This  is  less  than  the  mim% 

mum  adopted,  so  the  thickness  is  made  A  inch. 

PROBLEM 

What  thickness  of  web  is  required  for  a  shear  of  220,000  pounds,  depth  44 
inches? 

Before  the  thickness  of  web  can  be  accepted  as  being  satisfac- 
tory, it  must  be  known  to  provide  ample  bearing  for  the  rivets  which 


140  STEEL  CONSTRUCTION 

connect  the  flanges  to  the  web.  The  design  of  this  riveting  is  ex- 
plained later.  For  the  present  purpose  the  method  used  is  this: 
Assume  that  an  amount  of  stress  equal  to  the  maximum  vertical 
shear  must  be.  transmitted  from  the  web  to  each  flange  within  a 
distance  equal  to  the  depth  of  the  web.  Applying  this  to  the  exam- 
ple, the  maximum  vertical  shear  is  90,000  pounds  and  this  amount 
must  be  transmitted  from  web  to  flange  in  a  distance  of  48  inches, 
which  equals  the  depth  of  the  web.  The  bearing  value  of  a  J-inch 
rivet  in  a  ^-inch  web  is  5860  pounds.  The  number  required  is 

90000 

—  ^-—  or  16.    This  number  of  rivets  in  a  distance  of  48  inches  gives 

OobO 

a  spacing  of  3  inches,  which  is  satisfactory  and  requires  only  one  row 
of  rivets.  (Two  rows  could  be  used,  giving  space  for  twice  as  many 
rivets  as  are  needed.)  Therefore,  the  web  thickness  is  satisfactory. 

Shearing  Value  of  Web  Plates.  A  study  of  the  shearing  value 
of  web  plates  compared  with  the  bearing  value  of  rivets  in  the  web 
will  show  that  sufficient  bearing  value  can  be  developed  to  equal  the 
shearing  value.  Consequently,  the  bearing  test  need  not  be  applied. 
For  a  unit  shear  of  10,000  pounds  per  square  inch  and  a  unit  bearing 
of  25,000  pounds  per  square  inch,  it  can  be  shown  that  two  rows  of 
f-inch  rivets,  spaced  3f  inches  center  to  center  in  each'  row,  will  have 
the  same  bearing  value  as  the  shearing  value  of  the  plate  (no  reduc- 
tion being  made  in  shearing  value  on  account  of  rivet  holes). 
PROBLEM 

Assume  a  plate  64  inches  deep  and  i  inch  thick.  Prove  the  foregoing 
statement, 

Moment  of  Inertia  Required.  Having  the  bending  moment 
and  the  depth  of  the  girder,  the  value  of  the  required  moment  of 
inertia  can  be  computed  from  the  formula,  (see  p.  78). 

,    Me 
.  "  S 

In  the  example,  Fig.  114,  M  =  12,150,000  in.-lb.;  S  =  16,000  #.  If 
no  flange  plates  are  used,  the  distance  c  is  measured  to  the  back  of 
the  angle,  i.  e.,  24J  inches.  Then 


If  it  develops  that  flange  plates  must  be  used,  the  value  of  the  moment 
of  inertia  must  be  increased  to  correspond  to  the  increased  depth. 


STEEL  CONSTRUCTION 


141 


Flange  Section.  Having  determined  the  moment  of  inertia 
required,  it  is  next  necessary  to  find  by  trial  the  section  which  has 
this  moment  of  inertia.  To  avoid  tedious  figuring,  a  rough  approxi- 
mation is  first  made.  The  web  plate  being  determined,  its  moment 
of  inertia  may  be  computed  or  be  taken  from  the  handbook. 

7  for  PL  48"  X  A"  =  2880 

This  amount  deducted  from  18,415  leaves  15,535  as  the  net  value 
of  7  to  be  supplied  by  the  flanges.  The  general  formula  for  moment 
of  inertia,  p  38,  is 


15  535 

' 

oUo 


In  this  case  r  is  about  22.5  inches,  then  r2  =  506,  and  A= 

or  30.7  square  inches.  This  is  the  net  area 
of  the  two  flanges.  The  gross  section  must 
be  larger  to  allow  for  rivet  holes;  for  this 
add  2.3  square  inches,  making  33.0  square 
inches,  or  16.5  square  inches  for  each 
flange.  This  area  may  be  made  up  of  2 
angles  without  a  plate  or  of  2  angles  with  a 
plate.  Both  cases  are  given. 

Case  A—  Without  Flange  Plates.  With- 
out flange  plates,  use  2Ls  6"X6*Xf",  having 
an  area  of  2X8.44  or  16.88  square  inches. 
For  this  case  the  total  depth  is  48J  inches, 
as  previously  determined,  and  no  correc- 
tion is  needed  for  the  required  value  of  7, 
viz,  18,415.  Now  compute  its  value  for 
the  approximate  section,  Fig.  115,  making  Fig.  115.  Section  of  Plate  Girder 

Without  Flange  Plates 

the  necessary  corrections  for  rivet  holes. 

1  PI.  £8"  XTV  (from  tables)  ..............  2,880 

Deduct  for  holes  2X1  X  ft  X21  .75x21  .75    260      2,620 

4  Ls  6X6Xf  (from  tables)  about  axis  a-a        113 
about  axis  6-64x8.44x22.47x22.47   17,045 

17,158 
Deduct  for  holes  4XIX|X21.75X21.  75    1,241     15,917 

Total  net  value  of  /  18,537 


142 


STEEL  CONSTRUCTION 


In  deducting  for  rivet  holes,  the  diameter  of  hole  deducted  is  |  inch 

for  a  f-inch  rivet.    The  distance  to  the  holes  is  taken  at  the  outer 

of  the  two  rows  of  holes. 

The  moment  of  inertia  of  the  section  is  somewhat  larger  than 

the  required  amount,  therefore  the  section  is  satisfactory. 

Case  B — With  Flange  Plates.    With  flange  plates  it  is  usually 

specified  that  not  less  than  one-half  the  flange  area  shall  be  in  .the 
angles,  or  the  largest  size,  of  angle  shall  be 
used.  In  this  example  it  has  been  found 
that  only  one  row  of  rivets  is  necessary  for 
connecting  flange  to  web.  For  the  first 
trial  use  2Ls6"X4"Xf"  and  1  PI.  14"  X  A*. 
Then  the  gross  area  of  one  flange  equals 


for2Ls6"X4*Xf" 

for  1  PL  14' X  A" 

Total  area 


2X5.86  =  11.72 
=  6.12 
=  17.84 


The  section  is  shown  in  Fig.  116.  For  this 
section  the  value  of  c  is  24.25+0.44  or 
24.69.  The  required  value  of  /  must  be 
corrected  to  correspond: 

12,150,000X24.69 


16,000 


=  18,750 


Fig<11withSeFCb°nge0fpSesGirder  The  value  of  I  computed  for  the  assumed 
section  is 


1  PL  48' X  ft*  =    2880 

Deduct  for  holes  2XIX  ft  X21 .75X21 .75=      260       2,620 
4  Ls6"X4"Xf"  about  axis  a-a  =        30 

about  axis  b-b  4X5. 86X23. 22X23. 22        =12,637 

12,667 

2,296      10,371 

=  6,418 
=  19,409 


Deduct  for  holes 
4X|X|X21.75X21.75  =  1 
4X1X1X23.94X23.94  =  1260 
2  PL  14"XTV  less  2  rivet  holes 
2X12JXAX24.47X24.47 

Total  net  value  of  I 


STEEL  CONSTRUCTION  143 

This  value  of  7  is  in  excess  of  the  required  value,  the  latter  being 
18,750,  hence  the  section  may  be  reduced.  The  correction  can  be 
made  without  going  through  the  calculations  in  detail.  The  angles 
need  not  be  changed,  but  the  flange  plates  may  be  reduced  in  thick- 
ness. By  inspection  it  can  be  seen  that  a  reduction  of  ^  inch  in 
thickness  reduces  /  by  4  of  6418,  or  917.  The  resulting  net  value 
of  /  is  19,409-917  or  18,492.  This  reduction  in  the  thickness 
of  the  flange  plate  also  reduces  the  required  value  of  7.  It  now 
becomes 

7     12,150,000X24.63     1Q7nn 

16,000 

These  results  are  sufficiently  close  and  the  reduced  section  is  used 
although  it  is  somewhat  scant. 

The  revised  section  is 
x  web  plate  48"XTV 

/2Ls6"X4"Xf" 
each  flange  (lVLl*xr* 

The  sectional  areas  of  the  two  designs  are 

Case  A.  1  PI.  48 X  A  15.00  sq.  in. 
4Ls6x6Xf  33.76sq.  in. 

48.76sq.  in. 

CaseB.  1  PL  48 X  A  15. 00  sq.  in. 
4Ls6X4Xf  23.44sq.  in. 
2  PL  14 X f  10. 50  sq.  in. 

48. 94  sq.  in. 

This  showing  is  slightly  in  favor  of  Case  A,  but  it  is  more  favor- 
able to  Case  B  when  it  is  considered  that  the  flange  plates  do  not 
extend  the  full  length  of  the  girder.  Case  B  also  has  the  advantage 
of  greater  lateral  stiffness  due  to  its  greater  width.  On  the  other 
hand  the  cost  of  the  additional  riveting  may  amount  to  more  than 
the  saving  in  weight.  Also  the  use  of  the  flange  plates,  taking  into 
account  the  rivet  heads,  increases  the  over-all  depth  about  two 
inches,  which  may  be  objectionable  in  some  cases.  In  general,  the 
design  without  flange  plates  is  preferred. 

Width  of  Flange  Plates.  The  width  of  a  flange  plate  is  limited 
by  the  permissible  projection  beyond  the  outer  row  of  rivets.  The 
limits  are  eight  times  the  thickness  of  the  plate,  or  a  maximum  of 


144 


STEEL  CONSTRUCTION 


six  inches.  In  the  above  example  this  limit  is  8Xf"  or  3".  This 
permits  a  distance  of  8  inches  between  the  gage  lines,  which  is 
satisfactory. 

The  customary  widths  of  flange  plates  vary  by  2  inches,  thus, 
10-inch,  12-inch,  14-inch,  etc.     For  6-inch  flange  angles  the  maxi- 


Fig.  117.     Graphical  Method  of  Determining  Length  of  Flange  Plates,     (a)     For  Uniformly 
Distributed  Loads;  (b)     For  Concentrated  Loada 


mum  width  is  20  inches,  and  for  8-inch  angles,  24  inches,  but  18  and 
20  inches,  respectively,  are  preferable,  and  14  inches  and  18  inches 
are  most  used.  When  more  than  one  plate  is  used  on  a  flange, 
usually  the  outer  one  is  made  less  in  thickness  than  the  inner  one. 
Length  of  Flange  Plates.  The  flange  section  which  has  just 
been  computed  is  the  section  required  at  the  place  of  maximum 
bending  moment.  The  bending  moment  decreases  toward  the 
ends,  as  shown  in  the  moment  diagram  Fig.  114,  and,  if  it  were 


STEEL  CONSTRUCTION  145 

practicable  to  do  so,  the  flanges  might  be  decreased  correspondingly. 
It  is  necessary  for  practical  reasons  to  extend  the  flange  angles  the 
£ull  length  of  the  girder  but  the  flange  plates  can  be  stopped  at  the 
points  where  they  are  no  longer  needed.  The  plate  ceases  to  be 
needed  at  the  point  where  the  bending  moment  equals  the  resisting 
moment  of  the  web  plate  and  flange  angles.  This  can  be  computed 
by  the  methods  and  from  the  data  already  given,  but  the  process  is 
tedious  and  the  results  can  be  obtained  more  easily  by  graphical 
methods  with  sufficient  accuracy. 

Graphical  Solution  for  Uniformly  Distributed  Loads.  Let  Fig. 
117-a  represent  the  moment  diagram  for  any  uniformly  distributed 
load.  The  lines  at  1,  2,  3,  etc.,  represent  the  amount  of  the  bending 
moment  at  the  several  points  along  the  girder.  The  maximum 
bending  moment  is  at  5.  The  resisting  moment  is  represented  by 
the  line  o  c'.  This  line  is  divided  into  three  parts,  o  a  representing 
the  resisting  moment  of  the  web  plate,  a  b  the  resisting  moment  of 
the  flange  angles,  and  6  c'  the  resisting  moment  of  the  flange  plates. 
Then  the  distance  a1  a!  equals  the  theoretical  length  of  the  flange 
angles,  but  practically  they  are  made  the  full  length  of  the  girder, 
and  b'b'  equals  the  theoretical  length  of  the  flange  plates.  If  more 
than  one  plate  is  used  on  each  flange,  additional  divisions  may  be 
made  of  the  line  oc',  and  the  lengths  determined  in  the  same 
manner. 

If  the  resisting  moments  of  the  several  parts  of  the  flanges  have 
not  been  computed,  their  moments  of  inertia  may  be  used  for  this 
purpose  in  the  following  manner.  On  the  edge  of  a  sheet  of  paper 
or  on  a  scale  lay  off  at  any  convenient  scale  o  at,  aj)lt  and  6tCj 
equal,  respectively,  to  the  values  of  I  for  the  web  plate,  flange 
angles,  and  flange  plates.  Hold  the  zero  point  at  o  and  swing  the 
paper  or  scale  to  the  position  where  cv  falls  on  the  horizontal  line 
through  the  apex  of  the  moment  diagram  c'.  Then  the  horizontal 
lines  through  al  and  bl  will  cut  the  diagram  at  a'  d  and  br  b'  and 
give  the  lengths  of  flange  plates  required. 

Graphical  Solution  for  Concentrated  Loads.  Fig.  117-b  repre- 
sents a  moment  diagram  for  concentrated  loads.  The  same  explan- 
ations and  procedure  apply  as  for  uniformly  distributed  loads. 

Taking  the  girder  section  determined  for  Case  B,  p.  142,  the 
length  of  its  flange  plates  can  be  determined  by  the  method  just 


146  STEEL  CONSTRUCTION 

described,  using  the  moment  diagram  in  Fig.  114.    The  values  of  7, 

as  computed  on  p.  143,  are 

for  web  plate 2,620 

for  flange  angles 10,371 

for  flange  plates • 5,501 

18,492 

Using  a  convenient  scale  lay  off  o  cl  equals  18,492,  so  that  ct  falls  on 
the  horizontal  line  through  c'.  Then  divide  o  ct  at  al  and  bl  so  that 
0^  =  2620,  04^-10,371,  and  6,^=5501.  Draw  horizontal  lines 
through  al  and  blt  cutting  the  moment  diagram  at  a'  a'  and  6 '6'. 
Then  a'  a'  and  b'  b'  represent  the  theoretical  lengths  of  the  flange 
angles  and  the  flange  plates,  respectively.  As  previously  stated, 
the  flange  angles  always  extend  the  full  length  of  the  girder.  The 
flange  plates  are  usually  made  two  or  three  feet  longer  than  theo- 
retically required.  In  this  case  the  length  b'  b'  is  23'-6"  (approx.); 
the  plates  are  made  26'-0"  long.  This  extra  length  is  used  so  that 
some  stress  can  be  developed  in  the  plate  at  the  points  &'  &'. 

Web  Stiff eners.  Schneider's  Specifications*  provide  "The  web 
shall  have  stiffeners  at  the  ends  and  inner  edges  of  bearing  plates, 
and  at  all  points  of  concentrated  loads,  and  also  at  intermediate 
points,  when  the  thickness  of  the  web  is  less  than  one-sixtieth  of 
the  unsupported  distance  between  flange  angles,  generally  not 
farther  apart  than  the  depth  of  the  full  web  plate,  with  a  minimum 
limit  of  5  feet." 

The  theory  of  stresses  concerned  in  the  design  of  stiffeners  is  too 
complicated  for  consideration  in  this  text,  but  some  simple  rules  can 
be  established  which  will  lead  to  safe  construction.  Web  stiffeners 
may  be  divided  into  two  distinct  classes:  (1)  stiffeners  at  loaded 
points  and  (2)  intermediate  stiffeners. 

Stiffeners  at  Loaded  Points.  The  chief  purpose  of  stiffeners  at 
loaded  points  is  to  transmit  the  loads  to  the  girder  web.  According 
to  the  theory  of  stresses  in  girders,  the  load  must  be  applied  to  the 
web  and  produce  shear  therein  from  which  tension  and  compression 
are  produced  in  the  flanges.  It  is,  therefore,  necessary  to  carry  the 
applied  loads  into  the  web  plate  as  directly  as  possible.  If  the  load 
is  uniformly  distributed  on  either  the  top  or  bottom  flange,  it  is 

*"The  Structural  Design  of  Buildings"  by  C.  C.  Schneider,  M.  Am.  Soc.  C.  E.,  Transactions 
American  Society. of  Civil  Engineers,  Vol.  LIV,  p.  495. 


STEEL  CONSTRUCTION 


147 


transmitted  to  the  web  by  the  rivets  connecting  the  flange  angles 
to  the  web.  The  effect  of  this  load  on  the  number  of  rivets  required 
is  considered  later  in  the  text. 

When  concentrated  loads  are  applied,  enough  rivets  cannot  be 
placed  in  the  flanges  to  transmit  the  load  to  the  web,  and  also  it  is 
desirable  that  the  load  be  applied  throughout  the  depth  of  the  web 
plate.  To  meet  these  conditions  stiff ener  angles  are  used.  These 

/6QOOO  LBS 


Fig.  118.     Details  of  Girder  Showing  Use  of  Stiffeners  Under  Concentrated  Load 

stiffeners  may  be  designed  as  short  compression  members  using  a 
unit  stress  of  12,000  pounds  per  square  inch.  They  must  be  at- 
tached to  the  web  plate  with  enough  rivets  to  transmit  the  load. 
Generally  the  bearing  value  of  rivets  in  the  web  plate  will  govern. 

As  an  example,  assume  that  a  girder  supports  a  concentrated 
load  of  160,000  pounds,  Fig.  118.  On  account  of  the  width  of 
bearing  of  the  load,  it  is  desirable  to  use  two  pairs  of  stiffeners.  The 


148 


STEEL  CONSTRUCTION 


160  000 
area  required  is        '    --  or  13.33  square  inches.    4  Ls5rX3i*X  ft" 


—  area  4X3.53  or  14.12  square  inches— provide  the  necessary 
sectional  area.  The  thickness  of  the  girder  web  being  f  inch,  the 
bearing  value  of  .a  f-inch  rivet  is  7030  pounds.  Then  the  number 


160,000 
7030 


or  23.    There  is  ample  space  for  this 


of  rivets  required  is 

number  of  rivets. 

The  condition  at  the  end  bearing  of  a  plate  girder  is  analogous 
to  that  described  for  a  concentrated  load  and  is  treated  in  the  same 
manner.  If  the  end  of  the  girder  connects  to  a  column  or  another 
girder  by  means. of  web  angles,  the  design  is  made  in  the  same 
manner  as  for  the  web  connection  of  I-beams. 

Intermediate  Stiff eners.  Intermediate  stiff eners 
are  used  to  prevent  buckling  of  the  web  plate.  Ac- 
cording to  the  specifications  quoted  above,  stiffeners 
must  be  used  if  the  unsupported  depth  of  plate  is 
more  than  60  times  its  thickness.  Such  stiffeners 
are  to  be  spaced  not  farther  than  the  depth  of  the 
girder,  or  for  deep  girders  not  more  than  5  feet. 
Applying  this  to  the  girder  illustrated  in  Fig.  118, 
it  is  found  that  stiffeners  are  required,  for  the  unsup- 
ported depth  is  36  inches,  while  60  times  the  thick- 
ness |  inch  is  22J  inches.  The  depth  of  the  girder 
is  4  feet,  so  the  stiffeners  are  spaced  4  feet. 
Stiff  eners,  at  loaded  points  serve  incidentally  to  stiffen  the  web 
and  are  taken  into  account  in  spacing  the  intermediate  stiffeners. 
Intermediate  stiffeners  are  usually  angles-  in  pairs.  The  leg  of  the 
angle  parallel  to  the  web  plate  need  be  only  wide  enough  for  rivet- 
ing, say  3  inches,  as  it  adds  but  little  to  the  lateral  stiffness.  The 
outstanding  leg  must  be  determined  arbitrarily.  For  a  30-inch 
girder,  3  inches  may  be  used;  and  for  a  90-inch  girder,  6  inches;  and 
others  in  proportion.  The  thickness  should  be  consistent  with  the 
size  of  the  angle  and  not  less  than  the  thickness  of  the  web  plate; 
and  the  width  of  the  outstanding  leg  should  be  somewhat  less  than 
the  outstanding  leg  of  the  flange  angles 

Stiffeners  at  loaded  points  must  be  ground  to  fit  accurately 
against  the  loaded  flange;  intermediate  stiffeners  need  not  be  so 


Fig.  119.     Crimped 
Stiffeners 


STEEL  CONSTRUCTION  149 

carefully  fitted.  The  use  of  fillers  under  stiff  ener  angles  is  not 
necessary,  but  a  better  fit  can  be  obtained  when  they  are  used. 
This  makes  it  desirable  to  use  them  at  loaded  points  and  end  bear- 
ings. Where  fillers  are  not  used,  the  stiffener  angles  must  be  crimped 
to  fit  the  flange  angles,  Fig.  119.  There  is  little  difference  in  cost, 
as  the  expense  of  crimping  offsets  the  cost  of  the  filler  plates. 

Refer  to  the  girder  in  Fig.  114.  There  being  no  concentrated 
loads,  stiffeners  at  loaded  points  are  required  only  at  the  end  bearings, 
The  reaction  at  each  end  is  90,000  pounds.  The  area  of  stiffener 


angles  required  is  Or  7.5  square  inch.    4  Ls  3J'  X  3"  X  A"  have 


sufficient  area,  but  it  is  desirable  to  have  them  approximately  as 
wide  as  the  flange  angles,  so  4  Ls  5*X3"X  ft*  are  used.  Sixteen 
rivets  are  required.  There  is  ample  space  for  them. 

The  web  plate  is  ft  inch  thick  and  has  an  unsupported  depth 
of  36  inches,  hence  it  requires  intermediate  stiffeners.  These  are 
spaced  about  4  feet  apart  (equal  to  the  depth  of  the  girder).  Angles 
4"X3"X  ft*  may  be  used  for  these  stiffeners. 

Rivets  Connecting  Flange  Angles  to  Web.  In  order  to  make 
the  several  pieces  of  the  plate  girder  act  as  a  unit,  they  must  be 
rigidly  connected.  It  is  evident  that  if  the  angles  and  plates  were 
simply  placed  in  their  relative  positions  without  being  riveted,  they 
would  not  co-operate  but  would  tend  to  act  independently.  This 
is  explained  under  Horizontal  Shear  in  "Strength  of  Materials," 
Part  II. 

Number  of  Rivets.  The  loads  on  the  girder  are  applied  either 
directly  or  indirectly  to  the  web,  producing  vertical  shear.  By 
flexure,  the  vertical  shear  produces  horizontal  shear,  which  becomes 
tension  and  compression  in  fibers  below  and  above  the  neutral  axis, 
respectively.  Most  of  these  stresses  occur  in  the  flange  plates  and 
angles  and  must  be  transmitted  to  them  from  the  web  by  the  rivets 
which  connect  the  angles  to  the  web  plate.  There  must  be  enough 
rivets  to  transmit  the  whole  amount  of  the  stress  and  they  must  be 
located  at  the  points  where  the  stress  should  pass  from  the  web  to 
the  flanges.  Then  in  each  flange  there  must  be  such  a  number  of 
rivets  between  the  point  of  maximum  flange  stress  (maximum 
moment)  and  each  end  to  transmit  the  total  flange  stress;  or,  stated 
in  other  terms,  the  resisting  moment  of  the  rivets  between  the  point 


150  STEEL  CONSTRUCTION 

of  maximum  bending  moment  and  each  end  must  equal  the  maxi- 
mum bending  moment,  and  this  equals  the  resisting  moment  of  the 
girder  section, 

In  Fig.  118,  let  d  be  the  average  distance  between  the  rivets  in  the 
top  and  bottom  flanges;  k  the  bearing  value  of  one  rivet  (usually  bear- 
ing in  the  web  plate)  ;  M  the  bending  moment  in  inch-pounds;  and  N 
the  number  of  rivets  in  one  end  of  one  flange.  Then  k  Xd  equals  the 

resisting  moment  of  one  pair  of  rivets  in  inch-pounds  and  N 


equals  the  number  of  pairs  or  the  number  of  rivets  in  each  flange 
from  the  center  or  point  of  maximum  bending  moment  to  either 
end.  For  example,  assume  the  following  data: 

M  =450,000  ft.-lb.  =  5,400,000  in.-lb. 

k  =7030$,  bearing  value  of  a  f-inch  rivet  in  a  f-inch  web 

d  -41" 

Ar    5,400,000 
then  * 


Rivet  Spacing  in  Flanges.  If  the  rivets,  Fig.  117-a  and  -b,  were 
spaced  uniformly,  their  resisting  moment  would  be  represented  by  the 
moment  diagram  o'  c'  o',  whereas,  the  bending  moment  diagram  is 
o'  a'  b'  c'  b'  a'  o'.  From  this  it  is  clear  that  the  resisting  moment  of 
the  rivets  is  less  than  the  bending  moment  at  all  points  except  at  the 
maximum.  But  these  rivets  can  be  so  spaced  that  the  two  moment 
diagrams  will  coincide.  To  determine  this  spacing  proceed  as 
follows:  Lay  off  oN  equal  to  the  total  value  of  the  number  of  rivets, 
say  19,  and  divide  it  into  19  spaces  at  the  points  s.  Through  the 
points  s,  draw  horizontal  lines  intersecting  the  moment  diagram  at 
p'oints  t  .  Through  the  points  t,  draw  vertical  lines  intersecting  the  base 
line  at  the  points  r.  Then  the  points  r  are  the  locations  of  the  rivets. 

It  is  important  to  note  that  the  rivets  are  closer  together  near 
the  ends,  i.  e.,  where  the  bending  moment  is  changing  rapidly.  On 
the  left  side  of  Fig.  117-b,  the  spaces  are  nearly  equal  because  this 
side  of  the  moment  diagram  is  nearly  a  straight  line.  There  is  a 
change  of  spacing  wherever  there  is  a  change  in  direction  of  the 
moment  diagram.  For  the  uniform  load,  Fig.  117-a,  there  is  a 
change  in  each  space.  Of  course  it  is  not  practicable  to  space  the 
rivets  strictly  in  accordance  with  the  theory.  The  practical  method 


STEEL  CONSTRUCTION 

is  to  divide  the  girder  into  sections,  usually  taking  the  divisions 
formed  by  the  stiffeners,  and  space  the  rivets  equally  in  each  division. 

In  the  problem,  Fig.  114.  use  the  following  data:  , 

M  =  12,150,000  in.-lb. 

k  =5800 #,  bearing  value  of  a  f-inch  rivet  in  a  &-inch  web 
d  =41.26"  (Case  A,  Fig.  115) 

Ar      12,150,000      ,n   . 
thcn  ^  "5860X41. 26^°nVetS 

Lay  off  oN  equals  50.  Along  oof  lay  off  the  points  /,  29  3, 
etc.,  marking  the  positions  of  the  stiffeners.  Through  these  points 
draw  verticals  intersecting  the  moment  diagram  at  tv  t2,  etc.;  thence 
draw  horizontals  intersectinjg  o  N  at  sv  s2,  ss,  etc.  Then  o  sl  repre- 
sents the  number  of  rivets  between  o  and  1 ;  st  s2,  the  number  between 
1  and  2\  s2  s3  the  number  between  2  and  5;  etc. 

o  sl  represents  17  rivets;  the  distance  o'-l  is  64  inches;  space  the 
rivets  3  inches  center  to  center. 

$j  s2  represents  14  rivets;  the  distance  1-2  is  48  inches;  space 
the  rivets  3J  inches  center  to  center, 

s2sd  represents  10  rivets;  the  distance  $-$ia  48  inches;  space  the 
rivets  4£  inches'center  to  center. 

s3s4  represents  7  rivets;  the  distance  3-4  is  48  inches;  space  the 
rivets  6  inches  center  to  center,  and  this  being  the  maximum  spacing 
allowed,  continue  it  to  the  center  of  the  span. 

If  Case  B  be  used,  the  procedure  is  just  the  same.  The  value 
of  d  would  be  larger  (Fig.  116)  and,  consequently,  the  number  of 
rivets  smaller. 

Riveting  for  Cover  Plates.    In  Case  'B  there  must  also  be  deter- 
mined the  necessary  riveting  for  attaching  the  cover  plates  to  the 
flange  angles.    The  procedure  is  similar  to  that  just  given.     In 
Fig.  114,  p  c'  represents  the  resisting  moment  of  the  cover  plates  and, 
therefore,  the  required  resisting  moment  of  the  rivets.    The  rivets 
are  in  single  shear,  and  the  moment  arm  is  the  distance  back  to 
back  of  flange  angles.     Use  the  following  data: 
A/  =  3,600,000  in.-lb.  (approx.). 
k  =4420#,  single  shearing  value  of  a  ^-inch  rivet 
d  =481"  (Fig.  116) 

Ar         3,600,000 


152  STEEL  CONSTRUCTION 

Lay  off  p  A7!  equals  17.  Along  6'  &'  lay  off  the  points  10,  11, 
etc.,  at  intervals  of  say  4  feet.  Draw  verticals  to  £JO,  £„,  etc.,  and 
horizontals  to  #10,  sn,  etc. 

pslo  represents  9  rivets;  the  distance  b'-W  is  48  inches.  There 
are  two  rows  of  rivets  in  the  flange  plate,  so  there  are  4|  rivets 
required  in  one  row  in  48  inches,  i.  e.,  spaced  about  10  inches,  center 
to  center.  But  the  maximum  allowable  spacing  is  6  inches,  center 
to  center,  and  this  is  used  throughout  the  length  of  the  cover  plates 
except  at  the  ends  where  a  spacing  of  4  inches  for  a  distance  of  two 
feet  is  adopted  arbitrarily. 

Rivet  Spacing  Computed  from  Web  Bearing.  The  method,  p.  140, 
for  checking  the  thickness  of  the  web  plate  for  rivet  bearing  may  be 
used  for  determining  the  rivet  spacing;  for  example,  assume  that  an 
amount  of  stress  equal  to  the  vertical  shear  must  be  transmitted  from 
the  web  to  each  flange  within  a  distance  equal  to  the  depth  of  the  web. 
Then  the  number  of  rivets  required  in  this  distance  is  determined 
by  dividing  the  vertical  shear  by  the  bearing  value  of  one  rivet. 

Referring  to  Fig.  114  and  applying  this  method: 

Shear  at  0'  =  90,000  #  90,000 

—  =10,  spacing  about  3" 
No.  of  rivets  in  48  5860 

Shear  at  1  =  72,000  #  72,000 

XT      e  -    A   •    AO*  *  13,  spacing  about  3 J* 

No.  of  rivets  in  48  5800 

Shear  at  2  =  56,000  #  56,000 

XT       t   •     ±    •     AO*  =10,  spacing  about  4 J 

No.  of  rivets  in  48*  5860 

Shear  at  3  =40,000  #  40,000 

XT       »   .     A    .    '    „  • =   7,  spacing  about  6" 

No.  of  rivets  in  48  5860 

Spacing  when  Load  Transmitted  through  Flange  Rivets  into  Web. 
If  the  load  on  the  girder  is  applied  in  such  a  way  that  it  must  be 
transmitted  through  the  flange  rivets  into  the  web,  then  the  rivet 
spacing  must  take  this  into  account.  The  exact  method  of  doing 
so  is  difficult  to  apply,  but  safe  results  can  be  obtained  by  simply 
adding  enough  rivets  to  transmit  the  load  to  the  web.  Thus  in  Fig. 
114  it  has  been  determined  that  17  rivets  are  required  between  o'-l. 
The  load  on  this  space  is  18,000  pounds,  which  requires  4  rivets  to 
transmit  it  into  the  web  plate.  Then  the  total  number  of  rivets  is 
21  and  the  spacing  2\  inches. 


STEEL  CONSTRUCTION 


153 


Assuming  that  the 
load  is  applied  on  the  top 
flange,  the  extra  rivets  are 
required  only  in.  that 
flange.  But  in  practice 
the  riveting  is  usually 
made  the  same  in  both 
flanges.  Where  stiffeners 
are  used  at  loaded  points, 
the  extra  rivets  are  not 
required. 

The  actual  location 
and  spacing  of  the  rivets 
must  be  worked  out  in 
making  the  shop  details 
in  order  to  afford  neces- 
sary clearances  from  stiff- 
eners and  to  suit  any 
other  conditions  that 
may  apply  to  the  case. 
It  is  sufficient  for  the  de- 
signer to  indicate  the 
spacing  as  it  has  been 
computed  above. 

Fig.  120  shows  the 
design  drawing  for  the 
girder  developed  in  the 
preceding  pages,  using 
Case  B,  that  is,  a  girder 
with  flange  plates. 

PROBLEMS 

1 .  Design  a  plate  girder 
from  the  data  given  in  Fig. 
121.    Make  the  design  draw- 
ing at  f-inch  scale. 

2.  Design  a  plate  girder 
having  the  same  span  as  the 
one  in  Fig.  121,  but  support- 
ing  only   one-half  the  load 
there  specified. 


154 


STEEL  CONSTRUCTION 


Tables  and  Diagrams.    A  number  of  tables  have  been  pub- 
lished giving  strength  and  properties  of  plate  girders.    These  tables 


BJ?ICK  WALL 

'LAID  in  CEMEHT  MORTAR 


Fig.  121.     Data  for  a  Plate  Girder  Design 


are  of  much  assistance  in  arriving  at  the  approximate  section  of  the 
required  girder,  but  usually  the  final  design  must  be  computed  in 
detail,  as  in  the  foregoing  example. 


MOMENT  OF  INERTIA 

Fig.  122.     Diagram  for  Determining  Moments 
After  Deducting  Rivet  Holes.     2  Holes,  H"  (%"  Rivets)  for  %" 


The  large  number  of  plate  girder  sections  that  it  is  possible  to 
make  up  from  the  available  sizes  of  web  plates,  flange  angles,  and 
flange  plates  makes  it  impracticable  to  have  complete  tables  of  them. 
The  Carnegie  Pocket  Companion,  1913  edition,  contains  a  valuable 


STEEL  CONSTRUCTION 


155 


table  giving  the  section  modulus  for  a  large  number  of  riveted 
girders. 

The  handbooks  give  tables  of  the  moment  of  inertia  of  rectangles 
from  which  can  be  taken  the  value  of  7  for  the  web  plate  (from 
this  value  must  be  deducted  the  value  of  /  for  rivet  holes).  Other 
reference  books  give  the  values  of  7  for  web  plates  with  rivet  holes 
deducted  and  for  many  sizes  of  flange  angles  placed  at  various 
depths;  similar  tables  are  given  for  flange  plates.  By  the  use  of 
these  tables,  the  value  of  7  for  the  complete  girder  section  can  be 
found  by  adding  together  the  values  for  the  web  plate,  flange  angles, 
and  flange  plates.* 

The  diagrams,  Figs.  122,  123,  and  124,  give  respectively,  the 
values  of  7  for  web  plates,  flange  angles,  and  flange  plates.'  They 
give  the  moments  of  inertia  for  the  sizes  of  plates  and  angles  most 


Enter  diagram  at  left  margin  with  depth  of-  we  opiate  Trace  horizontally 
to  trie  diagonal  line  representing  the  assumed  thickness  of  the  plate, 
thence  vert/ca/ly  to  the  bottom  margin  and  read  the  moment  of  inertia 


MOMENT  OF  INERTIA 
of  Inertia  of  Web  Plates  of  Plate  Girders 
to  i''  Plates;  2  liolea,  1"  d"  Rivets)  for  \"  to  1"  Plates 

commonly  used  for  plate  girders.    Values  for  intermediate  sizes  of 
plates  and  thicknesses  of  angles  can  be  interpolated.     Although  not 

"•"Godfrey's  Tables"  by  Edward  Godfrey,  M.  Am.  Soc.  C.  E. 

"Civil  Engineer's  Pocketbook"  by  Albert  I.  Frye,  S.  B.,  M.  Am.  Soc.  C.  E. 


156 


STEEL  CONSTRUCTION 


ill! 
iill 


=  OOOI 
006 
008 
001 
009 

00? 
OOt 


STEEL  CONSTRUCTION 


157 


158  STEEL  CONSTRUCTION 

mathematically  exact,  the  results  obtained  from  these  diagrams  are 
accurate  enough  for  designing,  and  will  lead  to  the  selection  of  the 
same  sections  as  would  be  determined  by  computation. 

The  tables  and  diagrams  give  only  the  sections  to  be  used  for 
the  girder.  The  flange  plate  length,  stiffeners,  end  connections, 
and  rivet  spacing  must  still  be  designed  by  the  methods  heretofore 
explained.  In  many  .cases,  these  latter  items  are  left  to  the  de- 
tailers;  but  they  are  properly  a  part  of  the  design  and  should  be 
worked  out  at  the  same  time  the  girder  section  is  determined,  as 
the  detailer  i&  not  likely  to  have  as  clear  an  understanding  of  the 
conditions  as  the  designer. 
PROBLEM 

Check  the  girder  sections  in  Figs.  115  and  116  by  means  of  the  diagrams  in 
Figs.  122,  123,  and  124. 

OTHER  FORMS  OF  RIVETED  GIRDERS 

The  discussion  and  examples  thus  far  have  dealt  with  the  plate 
girder.  The  principles  and  the  methods  involved  are  the  same  for 
all  forms  of  riveted  girders. 

I=Beams  with  Flange  Plates.  A  form  of  girder,  Fig.  111-a,  is 
used  when  shallow  girders  are  required  and  the  I-beams  are  not 
strong  enough.  This  often  occurs  in  joists  and  girders  of  a  floor 
when  it  is  desired  to  maintain  approximately  the  same  depth  for 
members  wrhich  carry  heavy  and  light  loads. 

Moment  of  Inertia.  To  determine  the  moment  of  inertia  of  the 
girder,  take  from  the  handbook  the  value  of  /  for  the  beam  and 
deduct  therefrom  the  value  of  /  for  the  holes  in  the  flanges;  add  to 
this  net  value  for  the  beam,  the  value  of  7  for  the  net  section  of  the 
flange  plates.  For  example  compute  the  moment  of  inertia  for 
15"I42#and2P1.8"Xf. 

/for  15"  I  42  #  442 

deduct  for  4  rivet  holes 
4XJX|X7.2X7.2  114 

328 
for  2  PI.  8"Xf"  after  deducting  rivet  holes 

2x6iXfX7.9x7.9  585 

Total  value  of  I  913 

Note  that  two  rivet  holes  are  deducted  from  each  flange  and  from 
each  plate.  If  the  rivet  holes  are  carefully  staggered,  only  one-half 


STKKL  CONSTRUCTION 


159 


TABLE  IV 

Moments  of  Inertia  of  I-Beams  with  Holes  in  Flanges 

(Hol<-s  for  3.i '"  rivets  computed  J/£*  diam.) 


SECTION 

MOMENTS  OF  INERTIA 

Grip,  or  Thick 
t.esa  of  Metal 
at  Hole 

Whole 

1  Hole  Out  of 
Each  Flange 

2  Holes  Out  ot 
Each  Flange 

27"!    83# 

2888.6 

2623.0 

2357.4 

.89 

24*1  100  # 

2380.3 

2149.0 

1917.7 

1.00 

24'I    80# 

2087.9 

1884.9 

1681.9 

.87 

2i"I 

1028.0 

1734.3 

1540.6 

.82 

21"! 

1227.5 

1090.0 

952.5 

.74 

20"! 

14G6.5 

1320.0 

1173.5 

.92 

20"!     65# 

1169.6 

1042.4 

915.2 

.79 

•   is-I 

1141.3 

1026.8 

011.3 

.90 

is'T 

705.6 

704.9 

614.2 

.69 

18*1 

733.2 

645.2 

557.2 

.67 

15"!     80  r 

795.5 

706.6 

617.7 

1.03 

i.y'I 

609.0 

536.6 

464.2 

.82 

151 

441.7 

385.3 

328.9 

.62 

15"!     3d-- 

405.1 

351.8 

298.5 

.59 

12"!     40  # 

268.9 

231.3 

193.7 

.66 

121     31  i- 

215.8 

184/5 

153.2 

.545 

12"!     L'7!.  - 

199.6 

169.9 

140.2 

.51 

10"!     2fi# 

122.  1 

102.7 

83.3 

.49 

9"!    21 

84.9 

70.2 

55.5 

.46 

S"I     iv-. 

56.9 

46.1 

35.3 

.425 

of  this  number  need  be  deducted.  The  shearing  value  of  the  web 
must  be  investigated  and  the  length  of  flange  plates  and  rivet  spac- 
ing computed  in  the  same  manner  as  for  plate  girders: 

PROBLEMS 

1»  What  is  the  resisting  moment  of  a  girder  made  of  one  IS"  I  53$  and 
two  flange,  plates  8" XT?  •  -^  * 

2.  A  beam  has  a  span  of  24  feet  and  supports  a  u.  d.  load  of  80,000  pounds. 
Design  the  beam  using  a  18*  I  55#  with  flange  plates.     Determine  length  of 
plates  and  rivet  spacing. 

3.  What  is  the  resisting  moment  of  a  20"  I   65$  with  two  |-inch  holes  in 
each  flange?     (Note  the  great  loss  of  strength  due  to  punching  holes  in  the  flanges.) 

The  moments  of  inertia  of  I-beams  with  holes  in  the  flanges  are 
given  in  Table  IV  and  of  flange  plates  in  the  diagram,  Fig.  123. 

Beam  Box  Girders.  Beam  box  girders,  Fig.  1 1 1-d,  are  designed 
in  just  the  same  way  as  single  I-beams  with  flange  plates.  They 
are  not  economical  and  should  be  u^ed  onlv  when  the  available 


160  STEEL  CONSTRUCTION 

depth  prevents  the  use  of  a  deeper  girder.    The  handbooks  give 
tables  of  strength  of  this  form  of  riveted  girders. 

PROBLEMS 

1.  Compute  the  moment  of  inertia  of  a  girder  made  of  two  I-beams 
24*X80#  and  two  plates  18*  Xf'. 

2.  Design  a  beam  box  girder  to  support  a  load  of  300,000  pounds  at  the 
middle  of  a  30-foot  span.     Use  24-inch  beams. 

3.  What  is  the  resisting  moment  of  a  girder  made  of  two  15*  Cs  33#  and 
two  plates  14' 


Plate  Box  Girders.  The  plate  box  girder,  Fig.  111-c,  needs  no 
explanation  as  to  the  method  of  design,  requiring  the  same  procedure 
as  the  plate  girder.  It  is  used  for  very  heavy  loads  when  the  depth 
allowed  is  greater  than  the  deepest  I-beam  but  not  sufficient  to  per- 
mit the  use  cf  a  girder  with  a  single  web.  It  is  to  be  noted  that  the 
rivets  connecting  the  flange  angles  to  the  webs  are  in  single  shear, 
hence  the  shearing  value  rather  than  the  bearing  value  of  the  rivets 
will  be  used  in  computing  rivet  spacing. 

PROBLEM 

Compute  the  moment  of  inertia  of  a  girder  made  of  two  web  plates  36*  X  %*> 
four  angles  6'  X6*  X  !',  two  flange  plates  22*  X  !*,  and  two  flange  plates  22*  X  H*- 

Unsymmetrica!  Sections.  Thus  far  in  the  discussion  of  riveted 
girders  the  sections  considered  have  been  symmetrical  about  the 
neutral  axis  and,  therefore,  the  neutral  axis  has  been  at  mid-depth. 
It  sometimes  happens  that  the  two  flanges  cannot  be  the  same. 
This  makes  the  computation  of  the  moment  of  inertia  more  difficult. 
Having  made  the  first  approximation  of  the  section,  it  is  necessary 
to  find  the  center  of  gravity  of  the  assumed  section,  p.  35,  and  then 
the  moment  of  inertia  about  the  neutral  axis  (through  the  center 
of  gravity),  p.  36. 

The  common  examples  of  unsymmetrical  sections  are  crane 
girders,  I-beam  lintels  with  one  flange  plate,  girders  requiring  extra 
lateral  stiffness  on  account  of  unsupported  top  flange,  and  I-beams 
with  rivet  holes  in  the  tension  flange  at  the  place  of  maximum 
bending  moment. 

In  designing  such  girders  the  flanges  are  made  as  nearly  equal 
as  practicable,  so  that  the  neutral  axis  may  be  near  mid-depth. 
Of  course  this  cannot  be  done  when  a  single  flange  plate  is  used  on 
an  I-beam.  With  the  exception  noted  above,  viz,  locating  the 


® 


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162 


STEEL  CONSTRUCTION 


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neutral  axis,  the  procedure  in 
designing  is  the  same  as  for 
symmetrical  girders. 

PROBLEMS 

1.  A  lintel  is  made  of  a  12*  I 
31 1/2#  and  a  plate  on  .the  top  flange 
12"  X  A".    What  is  the  moment  of 
inertia  of  the  section? 

2.  What  is  the  resisting  mo- 
ment of  a  15"  I  42#  which  has  two 
holes  for  f-inch  rivets  in  the  bottom 
flange? 

PRACTICAL  APPLICATIONS 

Girder  Supporting  a  Col= 
umn.  In  order  to  get  the 
rooms  in  the  lower  part  of  a 
building  arranged  satisfacto- 
rily, it  is  sometimes  desirable 
to  space  the  columns  differ- 
ently than  they  are  placed 
above.  This  makes  it  neces- 
sary to  carry  the  upper  col- 
umns on  girders.  Such  a  case 
is  shown  in  Plate  O,  p.  285. 
As  is  usual  in  such  cases,  the 
amount  of  vertical  space  avail- 
able is  limited  and  the  depth 
of  the  girder  is  fixed  by  other 
considerations  than  economy 
of  design.  The  top  is  limited 
by  the  floor  level  above,  it 
being  necessary  to  have  room 
for  fireproofing  and  for  the  fin- 
ished flooring.  The  bottom  is 
limited  by  the  clearance  re- 
quired for  the  floor  below.  The 
actual  depth  of  web  is  de- 
termined after  making  a  pre- 


STEEL  CONSTRUCTION 


163 


liminary  design  of  the  flanges  and  finding  the  approximate  thickness 
of  flange  plates. 


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PAH  CL  LOAD  10*  I9>  80*-  15,200                             ^ 

ii                                                                                        P^ 

T                  i                   A                   1!                   j. 
j                                                                                                                       i 

'*•-! 

Fig.  127.     Girder  for  Garage  Roof 

The  vertical  shear  is  so  large  that  a  single 
web  plate  would  have  greater  thickness  than  is 
desirable  and,  furthermore,  the  shape  and  posi- 
tion of  the  supporting  columns  would  make  the 
connection  of  a  single  girder  somewhat  difficult  to 
design.  This  leads  to  the  adoption  of  two  web 
plates. 

At  the  supporting  columns  it  is  desired  to 
connect  one  web  plate  to  each  flange  of  the  col- 
umn as  shown.  If  a  box  girder  were  used,  it 
would  be  difficult  to  erect  it,  hence  two  girders 
best  fulfill  the  conditions.  Having  settled  the 
above  points,  the  girder  is  designed  by  the  meth- 
ods which  have  been  given.  Plate  O  shows  the 
design  drawing  of  the  girder  and  Fig.  125  is  the 
shop  detail  drawing. 
PROBLEM 

In  the  first  story  of  a  building  it  is  necessary  to  omit 
a  column  and  support  the  upper  part  of  the  column  on  a 


Fig.  128.      Section  of 
Typical  Craae  Girder 


164 


STEEL  CONSTRUCTION 


.girder.  The  span  of  the  girder  is  36  feet.  The  load  is  540,000  pounds  applied 
at  the  center  of  the  span,  and  in  addition  to  this  there  is  a  u.  d.  load  from  the 
second  floor,  the  weight  of  girder  with  its  firoproofing  amounting  to  4200 
pounds  per  lineal  foot.  The  depth  available  is  50  inches.  Design  the  cross 
section  of  the  girder. 

Plate  Girder  Lintel.  Fig.  12G  shows  a  plate  girder  used  as  a 
lintel  over  a  driveway  into  a  building.  It  supports  the  wall  above 
and  the  floor  loads  which  bear  on  the  wall. 

Roof  Girder.  A  garage  roof  is  to  be  built  with  no  supporting 
columns,  so  it  must  be  carried  from  wall  to  wall  on  girders.  The 
roof  slab  rests  on  I-beams  which 


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BEAMING  PLATE 

Fig   129.     Plate  Girder  Bearing  on  Masonry     Fig.  130      Diagram  Showing  Web  Connection  of 

are  connected  to  the  girders.     The  dimensions  and  loads -are  given 
in  Fig.  127.    There  is  no  limitation  of  depth,  the  most  economical 
section  being  desired. 
PROBLEM 

Design  the  girder  for  the  conditions  given  above  and  make  design  drawing 
at  f-inch  scale.  ( 

Crane  Girders.  Crane  girders  do  not  belong  to  the  class  of 
buildings  now  under  consideration.  Fig.  128  represents  a  typical 
crane  girder  and  is  given  to  illustrate  the  use  of  an  unsymmetrical 


STEEL  CONSTRUCTION 


165 


FITTED 
ANCLC 


SEAT  ANCLE 
FF  EWE  ft  ANCLES- 
FILLER— 
MN   WEB 


section  of  girder.  The  stresses  in  a  crane  girder  and  the  design  are 
explained  under  Runway  Girders  in  "Roof  Trusses".  The  channel 
on  the  top  flange  is  required  to  give  lateral  stillness  to  the  girder  in 
order  to  resist  the  lateral  thrust  of  the  crane  when  the  carriage  is 
moving  crosswise  of  the  build- 
ing. It  also  serves  incidentally 
as  a  guard  rail. 
PROBLEM 

Locate  the  neutral    axis  of  the 
girder  illustrated  in  Fig.  128. 

DETAILS  OF  CONSTRUCTION* 
End  Bearings.  When  the 
end  of  a  girder  bears  on  ma- 
sonry, Fig.  129,  the  bearing  plate 
is  designed  in  the  same  manner 
as  for  beams.  With  riveted 
girders  it  is  much  more  fre- 
quently necessary  to  replace 
the  plain  bearing  plate  by  I- 
beams  to  spread  the  bearing 
along  walls,  than  when  the 
girder  is  an  I-beam.  A  sole 
plate  should  be  riveted  to  the 
bottom  of  the  girder.  It  stiffens 
the  flange  angles  and  furnishes 
a  more  even  bearing  surface 
than  the  angles.  In  high-grade 
work,  the  bottom  of  the  girder 
may  be  faced  before  the  sole  plate  is  attached. 

A  very  heavy  load  may  require  a  bearing  plate  thicker  than  it  is 
practicable  to  obtain.  Then,  if  it  is  not  desired  to  use  I-beam  grill- 
age, a  cast-iron  pedestal  may  be  used  similar  to  those  used  for 
columns.  The  method  of  designing  them  is  given  under  columns, 
p.  220. 

PROBLEM 

Design  the  end  bearing  for  the  girder  specified  in  Fig    114. 

*The  details  of  stiffener  angles,  filler  plates,  flange  plates,  and  i 
cussed  and  illustrated  in  the  preceding  pages. 


SECTION 


Fig.  131. 


of  Girder  to  Column 


tet  spacing  have  been  dia- 


166 


STEEL  CONSTRUCTION 


Connections  to  Columns.  Web  Angle  Connection.  The  con- 
nection of  a  girder  to  a  column  is  usually  made  with  web  angles. 
The  connection  is  designed  in  the  same  manner  as  for  I-beams.  The 
angle  legs  connecting  to  the  girder  web  should  be  wide  enough  to 


Fig.  132.    Diagram  Showing  Connection  of  Girder  to  Face  of  Column 

take  two  rows  of  rivets  and,  if  the  construction  is  heavy,  the  filler 
plate  should  be  wide  enough  to  take  a  row  of  rivets  beyond  the 
edge  of  the  angles,  Fig.  130.  The  end  angles  must  be  set  accurately 
to  the  correct  length  and  at  right  angles  to  the  axis  of  the  girder. 
In  railroad  bridge  construction  the  end  angles  ere  required  to  be 
faced  and,  to  allow  for  it,  the  angles  used  are  £  inch  thicker  than 


STEEL  CONSTRUCTION 


167 


otherwise  would  be  required.    This  should  be  done  on  heavy  work 
in  building  construction. 


F.LAHGC  PL,  I4"xi~  /        SPLICE  PL.  14* f 


0-  O- 


SPLICE  in  FLANGE:  PLATE. 


(6)  SPL  /C£  Iff  rL  AHGE  ^fiGL  US 


0    0    0000 

0000 


WCBPL. 


(c;  SPLICE  IN  WEB  PLATE. 

Fig.  133.     Diagrams  of  Splices  in  the  Members  of  a  Plate  Girder  Section 

Bracket  Connection. "  The  bracket  connection,  Fig.  131,  may 
be  used.  It  does  not  make  as  stiff  a  joint  as  the  web  connection  and 
should  not  be  used  unless  there  is  some  special  reason  for  it.  This 


168  STEEL  CONSTRUCTION 

type  of  connection  is  specially  applicable  to  box  columns  on  which  the 
brackets  must  be  riveted  before  the  column  is  assembled.  Other 
forms  of  connection  may  be  used  to  meet  special  conditions. 
Fig.  132  shows  a  connection  of  the  web  directly  to  the  face  of  the 
column. 

Splices.  It  is  self-evident  that  there  should  be  no  splice  in  a 
girder  section  or  in  any  of  its  members  unless  such  a  splice  is  abso- 
lutely necessary.  If  the  splicing  is  of  individual  members  rather 
than  the  whole  girder  section,  the  extra  work  is  done  at  the  shop 
instead  of  in  the  field  and,  therefore,  is  not  so  serious. 

Splicing  Due  to  Transportation  Difficulties.  The  splicing  of  an 
entire  girder  section  may  be  occasioned  by  transportation  condi- 
tions but  it  is  expensive  on  account  of  extra  material  and  field 
riveting  required,  and  cannot  be  considered  as  good  as  the  unspliced 
section.  A  girder  of  any  length  likely  to  occur  in  building  construc- 
tion can  be  shipped  by  rail,  so  that  the  matter  involves  only  the 
comparison  of  the  extra  freight  cost  with  the  cost  of  the  splice. 
But  transportation  by  boat  involves  not  only  the  extra  charge  for 
long  members  but  an  absolute  limit  to  the  length  that  can  be  stowed. 
The  designer,  if  not  familiar  with  freight  rates  and  rules,  must  inves- 
tigate them,  if  girder?  longer  than  36  feet  are  to  be  shipped. 

Splicing  Due  to  Members  Longer  than  Stock  Sizes.  The  individual 
members  of  a  girder  may  need  splicing,  due  to  inability  to  secure 
material  of  sufficient  length,  which  often  happens  when  material 
is  ordered  from  stock.  ^  This  indicates  the  desirability  of  consulting 
stock  lists  while  designing,  so  that  the  available  sections  may  be 
used.  The  rolling  mills  regularly  furnish  angles  60  feet  long  and  by 
special  arrangement  will  furnish  longer  lengths.  All  usual  sizes  of 
cover  plates  are  furnished  in  lengths  up  to  85  feet.  Web  plates  are 
most  likely  to  require  splicing.  Lists  of  extreme  sizes  are  given  in 
the  handbooks.  Greater  lengths  than  there  listed  can  be  secured 
from  some  mills,  but  it  is  safer  to  be  governed  by  these  lists  unless 
definite  arrangements  can  be  made  for  the  longer  plates. 

Full  Strength  Splices  for  Flanges.  Both  tension  and  compres- 
sion flanges  must  be  fully  spliced,  i.  e.,  the  entire  tension  or  com- 
pression must  go  through  the  splice  plates  and  angles  and  the  rivets 
by  which  they  are  attached.  In  this  case  no  reliance  is  placed  on 
abutting  ends  of  compression  members  as  is  done  in  columns. 


STEEL  CONSTRUCTION  169 

Figs.  133-a,  -b,  and  -c  show,  respectively,  splices  in  a  flange 
plate,  in  flange  angles,  and  in  web  plate. 

Splice  for  Flange  Plate.  Fig.  133-a.  The  flange  plate  is  14"  X  \". 
The  stress  must  be  carried  across  the  gap  by  a  single  plate  (assum- 
ing that  there  is  no  unused  capacity  in  the  flange  angles),  which  must 
not  be  less  than  14"Xi".  The  net  area  of  this  plate  after  deducting 
rivet  holes  is  12J*X|"  or  6.125  square  inches.  Its  tensile  value  is 
6.125  X  16,000  or  98,000  pounds.  The  splice  rivets  are  in  single  shear, 

98  000 
hence  the  number  required  on  each  side  of  the  joint  is 


Use  20  rivets. 

Splice  jor  Flange  Angles.  Fig.  133-b.  The  flange  angles  are  2 
Ls  6*X6"xr.  Their  area  is  2x7  11  or  14.22  square  inches,  which, 
after  deducting  one  rivet  hole  from  each  angle,  becomes  a  net  area  of 
13.  12  square  inches.  The  splice  plates  must  have  this  net  area.  It 
is  desired  to  splice  both  legs  of  each  angle  as  directly  as  possible, 
so  the  splice  plates  are  arranged  as  shown.  Their  sizes  and  net 
areas  are 

m     2  PI.    5"  Xf,  net  area  6  18 

n      1  PL  13"  Xf,  net  area  7.  03 

Total  13.21  sq.  in. 

From  these  values  the  number  of  rivets  can  be  computed  in  the 
usual  way,  noting  that  the  rivets  through  m  are  in  double  shear  and 
through  n  in  single  shear.  The  plates  m  must  extend  beyond  n  at 
each  end  far  enough  to  take  two  additional  rivets.  The  purpose  of 
this  is  to  relieve  the  angles  of  a  portion  of  their  stress  before  the  first 
holes  in  n  are  reached.  Otherwise,  in  designing  the  main  girder 
section  one  hole  additional  would  be  deducted  from  each  angle. 

Splice  for  Web  Plate.  Fig.  133-c.  The  web  plate  must  be  spliced 
to  transmit  shear  and  bending  according  to  the  amount  of  these 
stresses  where  the  splice  occurs;  if  at  the  place  of  maximum  bending 
moment,  only  the  bending  stresses  need  be  considered,  shear  being 
zero;  if  near  the  end  where  the  flange  angles  will  take  care  of  all  the 
bending  stresses,  then  only  the  shear  need  be  provided  for. 

Resistance  to  Bending.  The  necessary  resistance  to  bending 
can  be  furnished  by  a  flange  plate,  as  in  Fig.  133-a;  by  splice  plates 
on  the  angles,  as  plates  m  in  Fig.  133-b;  or  by  splice  plates  o  in  Fig. 


170 


STEEL  CONSTRUCTION 


133-c;  or  by  any  combination  of  them.  In  either  case  the  moment 
of  inertia  of  the  net  section  of  the  splice  plate  must  equal  that  of  the 
web  plate,  or  such  portion  of  it  as  is  needed  at  the  place  where  the 
splice  occurs.  It  must  be  noted  that  a  web  plate  which  must  be 
spliced  loses  some  of  its  moment  of  inertia  because  of  the  holes  for 
attaching  the  splice  plates;  consequently,  it  is  better,  if  practicable, 
to  use  a  form  of  splice  which  will  add  no  rivet  holes.  If  a  flange 
plate  is  used  as  a  part  of  the  girder  section,  then  an  additional  flange 
plate  may  be  used  for.  splicing  the  web.  If  there  is  no  flange  plate 
in  the  girder  section,  then  plates  such  as  ra,  Fig.  133-b,  may  be  used 
to  advantage  for  all  or  part  of  the  web  splice. 

Taking  for  example  the  girder  in  Fig.  116,  the  web  plate  is  48" 


Fig    134.     Splice  in  Plate  Girder 


Fig.  135.     Bracket  tor  Bracing 
Top  Flange  of  Girder 


X  ft*.     Its  net  moment  of  inertia  is  2620,  p.  141.    Two  flange  plates 
14"  X  J"  after  deducting  2  rivet  holes  from  each,  have  a  net  value  of_/ 

7  =  2Xl2JxiX24.  9X24.  9  =  3800 
which  is  more  than  required. 

Taking  the  girder  shown  in  Fig.  115,  if  a  flange  plate  should  be 
used  for  splicing,  the  angles  would  be  weakened  by  the  rivet  holes 
for  attaching  the  plate.  If  plates  such  as  m,  Fig.  133-b,  are  used, 
no  additional  rivets  are  needed.  Try  four  plates  5"Xf".  Their  net 
value  of  I  after  deducting  one  rivet  hole  for  each  is 


which  is  near  enough  to  be  satisfactory. 


STEEL  CONSTRUCTION 


171 


In  a  similar  manner,  plates  o,  Fig.  133-c,  are  found  to  be  G"X  ft* '. 
The  strength  of  the  splice  plate  must  be  developed  by  rivet  bearing 
in  the  web  plate  requiring   10  on  each 
side  of  the  joint.     Although  this  is  the 
most  direct  method  of  splicing  for  bend- 
ing, it  is  not  as  economical  as  either  of 
the  other  methods  given  above. 

Resistance  to  Shear.  For  resisting 
shear,  the  splice  plates  are  in  the  form  of  Q{ 
the  plates;?,  Fig.  133-c.  On  each  side  of  <3 
the  joint  there  must  be  enough  rivets  to 
transmit  the  total  shear.  They  may  be 
in  one  or  more  rows.  The  thickness  of 
each  plate  must  be  at  least  half  that  of  the  web  plate  and  is  sub- 
ject to  the  same  minimum.  Hence,  in  this  case  the  thickness  is 
made  ft  inch. 


Fig.  13G.     Brace  for  Plate  Girder 


Fig.  137.     Brace  for  End  Girder 


Position  of  Splices.  Girders  completed  in  the  shop  will  have  splices 
arranged  to  come  at  different  places;  thus  the  web  may  be  spliced  at 
the  center  and  the  angles  near  one  end ;  still  better,  one  angle  may  be 
spliced  on  one  side  of  the  center  and  the  other  on  the  opposite  side. 
Of  course,  in  a  field  splice  all  the  elements  are  joined  at  one  place. 
The  method  of  computing  is  the  same  as  has  been  given  for  the 
individual  parts  of  the  girder  (bearing  in  mind  that  the  rivets  are 


172  STEEL  CONSTRUCTION 

field  driven).    Fig.  134  illustrates  such  a  splice  made  up  from  the 
several  splices  shown  in  Fig.  133. 

PROBLEM 

Design  field  splice  for  plate  girder  shown  in  Fig  115. 

Lateral  Support.  Girders,  like  beams,  must  be  supported  later- 
ally to  prevent  the  compression  flange  from  buckling.  Schneider's 
Specifications  provide  that  "the  unsupported  length  of  flange  shall 
not  exceed  16  times  its  width.  In  plate  girders  used  as  crane  run- 
ways, if  the  unsupported  length  of  the  compression  flange  exceeds 
12  times  its  width,  the  flange  shall  be  figured  as  a  column  between 
the  points  of  support."* 

In  most  cases  the  lateral  support  is  provided  by  the  joists  or 
floor  construction.  Where  this  is  not  the  case,  the  supports  can  be 
provided  in  a  number  of  different  ways.  For  lengths  up  to  25  feet, 
the  necessary  stiffness  can  be  provided  by  the  use  of  wide  flange 
plates.  For  greater  lengths,  box  girders  may  be  used,  if  the  load 
warrants  their  use.  Fig.  135  shows  a  plate  girder  to  which  a  joist 
connects  near  the  bottom.  From  this  joist  a  bracket  extends  up  to 
and  supports  the  top  flange.  The  corner  brace  indicated  in  Fig. 
136  sometimes  may  be  used  to  advantage. 

As  provided  in  Schneider's  Specifications,  crane  girders  whose 
length  exceeds  12  times  the  width  must  be  designed  as  columns. 
The  method  is  the  same  as  given  hereinafter  for  columns. 

The  ends  of  the  girders  must  be  especially  well  secured  against 
overturning.  When  connected  to  columns  or  other  girders,  the 
desired  result  is  easily  attained  by  the  use  of  web  angles  or  top  con- 
nection angles.  If  the  end  rests  upon  and  is  built  into  masonry',  the 
required  support  is  thus  provided.  Fig.  137  shows  one  girder  rest- 
ing on  another  and  braced  thereto. 


*Transactions  American  Society  of  .Civil  Engineers,  Vol.  LIV,  p.  495 


MONROE  BUILDING,  CHICAGO 

Holabird  &  Roche,  Architects 


CONSTRUCTION 

PART  III 


COMPRESSION  MEMBERS— COLUMNS 
STEEL  COLUMNS 

Definitions.  A  column  (or  strut)  is  a  member  subjected  to 
compression  in  the  direction  of  its  longitudinal  axis,  i.  e.,  subjected 
to  axial  compression.  The  term  "column"  is  usually  applied  to  a 
vertical  member  subjected  directly  to  a  gravity  load.  The  com- 
pression members  of  trusses,  and  also  small  isolated  members,  and 
members  in  other  than  the  vertical  position,  are  called  "struts" 

A  series  of  columns  in  a  vertical  line  is  called  a  "stack". 

The  columns  in  any  one  story  of  a  building  constitute  a  "tier". 

Loads  and  their  Effects.  Computation  of  Loads.  The  loads  on 
a  column  are  applied  to  it  by  the  column  section  above  and  through 
the  connections  of  other  members  or  other  materials.  Most  com- 
monly this  is  through  beams  and  girders.  The  amounts  of  these 
loads  may  be  taken  from  those, previously  computed  for  the  beams 
and  girders,  or  may  be  computed  directly  from  the  floor  and  wall 
areas  tributary  to  the  column.  The  former  method  is  easier  when 
the  loads  and  areas  are  irregular,  and  the  latter  when  the  loads  are 
uniform  and  the  arrangement  of  beams  regular.  Practical  exam- 
ples of  computing  the  loads  are  given  later  in  this  book. 

The  ideal  condition  of  loading  of  a  column  is  had  when  the  load 
is  applied  uniformly  over  the  top  of  a  column,  and  when  the  bottom 
of  the  column  bears  evenly  on  its  support  or  foundation.  In  a 
stack  of  columns,  the  load  on  any  column  which  comes  from  the 
column  above  is  usually  applied  in  this  ideal  way.  But  the  other 
loads  are  generally  applied  to  the  sides  of  the  column  through  beam 
connections,  in  many  cases  with  greater  loads  on  one  side  than  on 
the  other. 


174 


STEEL  CONSTRUCTION 


} 

(°)                     (*>) 

"'ig.  138.      Diagram    Showir 
Examples  of  (a)  Concentric 

Loads  and  (b)  Eccentric 
Loads 


Loads  applied  centrally,  or  which  are  equally  balanced  on  oppo- 
site sides,  are  called  "concentric  loads",  Fig.  138-a.    Loads  applied 
t  I  to  the  sides  of  the  column  and  not  balanced, 

or  those  which  bear  on  top  but  are  not  cen- 
trally placed,  are  called  "eccentric  loads", 
Fig.  138-b.  These  terms  apply  to  the  bear- 
ing at  the  bottom  of  the  column  as  well  as 
to  the  loading  at  the  top,  but  usually  the 
bearing  at  the  bottom  is  made  uniform,  i.  e., 
concentric. 

Concentric  Loads.  Concentric  loads, 
Fig.  139,  produce  direct  or  axial  compres- 
sion in  the  column.  This  compression  may 
be  considered  as  evenly  distributed  over  the 
entire  cross  section,  even  if  the  loads  be 
balanced  loads  connected  to  opposite  sides 
of  the  column.  Then  the  unit  stress  P  on 
the  column  is  the  load  W  divided  by  the  area 
A  :  which  is  expressed  by  the  formula 

"5 

Conversely  the  capacity  of  a  column  or  its  total  permis- 
sible load  is  the  allowable  unit  stress  multiplied  by  the 
area: 

W=PA 

For  example,  assume  the  load  on  a  column  to  be 
190,000  pounds  and  the  area  of  the  assumed  column  16.4 
square  inches.  Then  the  unit  stress,  or  average  compres- 

.       .    190,000 
sion,  is  or  11.585   pounds  per  square  inch. 

Eccentric  Loads.  Eccentric  loads,  Fig.  140,  produce 
axial  compression  and  in  addition  cause  bending  stresses. 
The  axial  compression  is  determined  in  the  same  way 
as  for  concentric  loads,  and  the  bending  stresses  in  the 
same  manner  as  for  beams,  p.  81. 

The  bending,  or  eccentric,  moment  of  the  load  is  the  centric  Loads 
amount  of  the  load  multiplied  by  its  distance  from  the  neutral  axis  of 


Fig.  139.    Dia- 


STEEL  CONSTRUCTION 


175 


the  column.  The  sum  of  the  axial  compression  per  square  inch  and 
the  maximum  compression  fiber  stress  per  square  inch  is  the  maxi- 
mum combined  stress  resulting  from  the  eccentric  load.  (See  Flex- 
ure and  Compression  for  Beams,  in  "Strength  of  Materials",  Part 
II.)  This  is  illustrated  in  Fig.  140.  W  is  an  eccentric  load.  The 
direct  stress  in  the  column  is,  represented  by  the  area  abed  and 
equals  W.  (This  area  may  represent  the  total 
load  on  the  column  if  there  are  other  loads  than 
W.)  The  bending  moment  produces  the  com- 
pression  066'  and  the  tension  o  c  c'  .  Then  the 
maximum  fiber  stress  in  the  column  is  a  &',  being 
the  sum  of  a  6  and  b  b'.  On  the  side  opposite  to 
the  eccentric  load,  the  tension  due  to  bending 
overcomes  part  or  all  of  the  compression  due  ta 
direct  stress.  The  result  in  this  case  is  dcr',  but 
the  stress  in  this  side  of  the  column  rarely  needs 
consideration.  Of  course,  the  eccentricity  may 
be  so  great  that  the  opposite  side  of  the  column 
is  in  tension,  but  even  this  does  not  require 
attention  unless  the  column  is  spliced. 

The  total  stress  produced  by  all  the  loads 
equals  the  sum  of  the  stresses  produced  by  the 
loads  separately*.  Some  authorities  allow  three- 
fourths  of  the  bending  moment  to  be  used  hi 
computing  the  effect  on  the  column.  This  prac- 
tice is  satisfactory  and  is  followed  in  the  illus- 
tration used  later  in  this  book. 

Typical  Cases.  The  entire  load  on  the  col- 
umn,  including  its  own  weight  and  the  weight 
of  the  fireproofing,  must  be  determined  (making 
no  distinction  between  concentric  and  eccentric  loads).  Then 
compute  the  bending  moments  due  to  the  eccentric  loads, 
dividing  these  moments  between  the  respective  axes  of  the 
column. 

(a)    As  an  example,  refer  to  Figs.  139  and  140,  letting  them 
represent  the  same  column.    Assume  W  a  concentric  load  of  100,000 


7 

1 

lit 

i 

^xj 

tr 

.    140.       Diagram    of 

*Thia  statement  is  not  exactly  correct  but  represents  usual  practice. 


176  ,  STEEL  CONSTRUCTION 

pounds;  W  an  eccentric  load  of  50,000  pounds;  and  e  an  eccen- 
tricity, or  lever  arm  of  W,  of  10  inches.     Then 

Total  load  =  100,000+50,000=  150,000  # 
The  bending  moment  due  to  the  eccentric  load  is 
M  =  50,000X10  =  500,000  in.-lb. 

As  a  trial  section,  take  a  column  made  of  1  PI.  12"X|"  and 
4Ls  6"X3J"Xf"  from  which  c,  the  distance  from  the  neutral  axis  to 
the  extreme  fiber,  is  6.125  inches;  r,  the  radius  of  gyration  about 

the  same  axis  as  the  bending  moment,  is  5.00  inches;  -,  the  section 

c 

modulus,  is  74.7  inches3;  and  A,  the  area,  is  18.2  square  inches. 
The  average  stress  resulting  from  the  total  load  is 

150,000    co/,nj, 

-  18  2    =8240ff  persq.  in. 

This  is  represented  by  a  b  in  Fig.  140. 

The  maximum  fiber  stress  resulting  from  the  bending  moment, 
taking  three-fourths  of  the  computed  moment,  is 

fX500,000     CAOni, 

— - — ^ =  5020#  per  sq.  in. 

This  is  represented  in  Fig.  140  by  b  b'  and  c  c'  in  compression  and 
tension,  respectively. 

Then  the  total  maximum  fiber  stress  in  the  column  is 

8240+5020  =  13,260  #  per  sq.  in. 
This  is  represented  by  a  b'. 

The  method  of  determining  the  allowable  stress  has  not  yet 
been  given  so  it  cannot  be  decided  whether  the  trial  section  given 
above  is  satisfactory. 

(b)  Fig.  141  illustrates  cases  of  concentric  and  eccentric  load- 
ing. In  each  of  them  there  may  be  a  concentric  load  from  the 
column  section  above.  In  Fig.  141-a,  the  loads  are  concentric,  pro- 
vided those  on  opposite  sides  are  equal  and  balance  each  other. 
If  m  be  omitted,  o  becomes  eccentric,  but  as  it  connects  to  the  web 
of  the  column  the^  eccentricity  is  small  and  usually  is  neglected. 
If  n  be  omitted,  p  becomes  eccentric  with  a  moment  arm  e  and  a 
bending  moment  pXe.  If  n-  is  less  than  p,  the  difference  is  the 
eccentric  load  and  the  bending  moment  is  (p—n)  Xe.  In  Fig.  141-b, 
the  load  u  is  eccentric  about  the  axis  2-2,  and  the  bending  moment 


STEEL  CONSTRUCTION 


177 


is  uXer  The  resulting  fiber  stress  must  be  computed  from  the 
moment  of  inertia  about  the  same  axis.  The  load  v  is  eccentric 
about  the  axis  1-1,  and  the  bend- 
ing moment  is  tXer  The  result- 
ing fiber  stress  must  be  com- 
puted from  the  moment  of  inertia 
about  the  same  axis.  Both 
eccentric  loads  produce  compres- 
sion at  the  corner  d,  hence  the 
effects  of  both  must  be  added  to 
the  axial  stress  produced  by  the 
total  load,  in  order  to  determine 
the  maximum  fiber  stress  in  the 
column. 

As  an  example,  take  Fig. 
141-b  and  assume  the  following 
data,  taking  for  the  trial  section, 
a  column  made  of  1  PL  12"  Xf 

and  4  Ls  6"X3£"Xf  from  Which     Fig.    Ml      Diagrams    Showing    (a)  Concentric 

Load  and  (b)  Eccentric  Loads  on  Columns 

71  is  213;  72  is  721;  c,  is  6f;  c2  is 

6J";  et  is  7";  e2  is  9i";  and  A  is  29.7  sq.  in. 

Concentric  load  from  column  section  above  =  150,000 

t>=  30,000 
u  =  45,000 


Total  load 
Unit  stress  from  total  load 


=  225,000  # 
225,000    , 


29.7 


=  7575  #  per  sq.  in. 


Mi  =  30,000X7  =  210,000  in.-lb. 
f  of  this  =  157,500  in.-lb. 

TT  -*«u      *        A  157,500X6|     ,7on/i 

Unit  fiber  stress  due  to  v  =  -  —  —  -  -  =4720#  per  sq.  in. 

.-  lt> 

3/2  =  45,OOOx9i  =  416,000  in.-lb. 
f  of  this  =  312,000  in.-lb. 


Unit  fiber  stress  due  to  u  = 


2650  #  per  sq.  in. 
Total  fiber  stress  at  d  =  7575  +4720  +2650=  14,945  #  per  sq.  in. 


178  STEEL  CONSTRUCTION 

PROBLEM 

Assume  a  heavier  column  section  for  the  example  given  above'and  compute 
the  total  maximum  fiber  stress. 

Eccentric  Load  In  Terms  of  Equivalent  Concentric  Load.  The 
effect  of  the  eccentricity  of  the  load  can  be  expressed  in  terms  of  an 
equivalent  concentric  load,  which  can  be  added  to  the  actual  load 
and  the  resulting  total  be  applied  as  a  concentric  load,  giving 
the  same  maximum  stress  as  if  computed  by  means  of  the  bending 
moment.  The  proportion  to  be  added,  if  the  full  eccentricity  is 
used,  is  given  by  the  expression 

wt-wi& 

Or,  if  the  reduction  in  eccentricity  is  made  in  accordance  with  the 
rule  on  p.  175,  the  expression  is 


In  these  formulas  W  is  the  eccentric  load  and  We'  is  the 
equivalent  concentric  load.  Before  this  method  can  be  applied,  it 
is  necessary  to  select  the  trial  column  section,  and  from  it  compute 
the  values  of  c  and  r.  As  the  values  of  c  and  r  for  the  trial  section 
will  vary  but  little  from  those  for  the  final  section,  it  usually  will  be 
unnecessary  to  correct  the  equivalent  concentric  load  computed  by 
this  method. 

Referring  now  to  the  example  illustrated  in  Figs.  139  and  140 
and  explamed  on  p.  176,  the  eccentric  effect  is 


t 
5X5 

Then  the  total  equivalent  concentric  load  on  the  column  is 
W  =100,000 
W'=  50,000 
HY=  91,875 

241,  875  # 
and  the  resulting  stress  in  the  column  is 


This  result  agrees  closely  with  the  results  obtained  by  Use  of  the 
bending  moment.    It  would  agree  exactly  if  all  the  computations 


STEEL  CONSTRUCTION  179 

and  the  values  of  the  properties  were  given  in  more  exact  figures. 
Note  that  the  equivalent  concentric  load  is  not-  carried  down  into 
the  next  lower  section  of  column  but  disappears  at  the  bottom  of 
column  section  under  consideration. 

PROBLEM 

Compute  the  equivalent  concentric  load  and  the  resulting  unit  stress  for 
the  eccentric  loads  u  and  v  in  Fig.  141-b  from  the  data  given  on  p.  177. 

Strength  of  Columns.  The  ideal  column  is  perfectly  straight, 
symmetrical,  and  homogeneous,  but  these  conditions  are  never  fully 
attained.  The  material  may  not  be  exactly  straight,  then  inaccur- 
ate workmanship,  the  punching  of  rivet  holes,  driving  of  rivets, 
abuse  in  handling,  and  internal  defects  of  the  steel,  all  cp-operate 
to  produce  results  somewhat  short  of  ideal.  These  imperfections 
are  of  more  importance  with  long  than  with  short  columns,  and  like- 
wise with  small  columns  than  with  large  ones. 

The  fo'regoing  conditions  make  it  necessary  to  use  lower  stresses 
in  columns  than  are  used  for  beams;  also  to  vary  the  stresses  accord- 
ing to  the  length  and  size  of  the  column.  The  relations  cannot  be 
expressed  in  a  rational  formula,  that  is,  a  formula  deduced, from 
theory,  as  is  the  case  with  beams;  hence  empirical  formulas  are 
used,  i.  e.,  formulas  based  on  experimental  data.  A  large  number 
of  tests  have  been  made  to  determine  the  effect  of  the  length  and 
size  on  the  strength  of  columns.  Several  formulas  have  been 
derived  giving  results  agreeing  closely  with  the  tests. 

Formula  for  Unit  Stress.  The  simplest  of  these  formulas  and 
the  one  now  most  generally  used  is 

P  =  16,000-70- 
r 

in  which  P  is  the  permissible  compression  per  square  inch  of  cross 
section;  /  is. the  unsupported  length  of  column  in  inches;  and  r  is  the 
least  radius  of  gyration  in  inches.  The  radius  of  gyration  rather 
than  the  side  or  the  diameter  is  used  as  the  measure  of  the  size  of 
the  column  as  it  relates  more  directly  to  the  stiffness. 

From  the  above  formula  the  allowable  stress  per  square  inch 
can  be  determined  for  any  column  having  known  values  of  I  and  r. 
Thus  if/ =  180"  and  r  =  2.4" 

i&n 
P  =  16,000-70 =  16,000-5250- 10,750#  per  sq.  in. 


180  STEEL  CONSTRUCTION 

Then  the  total  capacity  W  equals  PxA  (p.174);  and  assuming 
A  =  l2.0sq.  in. 

\V  =10,750X12.0  =  129,000  # 

The  end  condition  of  the  column  has  some  effect  on  the  strength. 
A  column  which  has  ends  resting  on  pins  or  pivots  will  not  support 
as  great  a  load  as  one  which  has  flat  or  fixed  bearings.  The  formula 
given  above  applies  to  columns  with  flat  or  fixed  ends  and  as  these 
are  used  almost  universally  in  building  construction,  the  other 
formulas  need  not  be  considered  in  this  text.  Pivoted  and  pin  ends 
for  columns  occur  in  bridge  construction  and  the  necessary  formulas 
for  them  are  given  in  books  on  that  subject. 

The  values  given  by  the  formula  .do  not  apply  to  very  long  or 
very  short  columns.  The  maximum  value  of  P  allowed  (see  Unit 
Stresses,  p.  51)  is  14,000  pounds.  This  corresponds  to  a  value  of 

—  =  30,  so  14,000  must  be  used  when  —  is  equal  to,  or  less  than,  30. 
r  r'  . 

In  the  other  direction  the  limiting  value  of  —  is  120,  according  to  most 

specifications.  However,  larger  values  may  be  used  with  safety  if 
particular  care  is  taken  to  avoid  eccentricity. 

Schneider's  Specifications  provide  that  "No  compression  member 
shall  have  a  length  exceeding  125  times  its  least  radius  of  gyration, 
except  those  for  wind  and  lateral  bracing,  which  may  have  a,  length 
not  exceeding  150  times  the  least  radius  of  gyration/'* 

The  formula  takes  into  account  only  the  average  imperfections 
in  columns,  and  makes  no  allowance  for  the  different  styles  of 
columns.  Nevertheless,  It  is  known  that  columns  with  solid  web 
plates  are  more  efficient  than  laced  columns,  and  laced  columns  in 
turn  are  more  efficient  than  columns  writh  batten  plates.  There 
is  no  wrell-established  practice  in  reference  to  this  but  a  rea- 
sonable allowance  is  to  deduct  from  the  values  given  by  the 
formula  25  per  cent  for  laced  columns  and  50  per  cent  for  battened 
columns. 

Having  adopted  a  formula  by  which  the  allowable  unit  stress 
can  be  computed,  the  example  given  on  p.  17G  can  be  completed. 


*Transactions  American  Society  Civil  Engineers,  Vol.  LIV,  p.  495.  ; 


STEEL  CONSTRUCTION  181 

The  trial  section  there  used  was  a  column  made  of  1  PL  12"X|"  and 
4  Ls  6"X3i"Xf ,  from  which  r  (least  value)  is  2.56";  and  A  is  18.2 
sq.  in. 
Assume  /=102".    The  allowable  unit  stress  is 

P  =  16,000-70 -  =  16,000-70  4-— =  13,200#  per  sq.  in. 
r  2. on 

The  maximum  fiber  stress  computed  from  the  assumed  loading  is 
13,260  pounds  per  square  inch,,  hence  the  trial  section  is  satis- 
factory. 

Taking  the  example  on  p.  177,  the  trial  section  of  column  is 
made  of  1  PI.  12"Xf"  and  4  Ls  6"  X3i"Xf,  from  which  r  (least  value) 
is  2.6S";  and  A  is  29.7  sq.  in. 
Assume  /=  138".    -The  allowable  unit  stress  is 

TOO 

P  =16,000-70  ~-  =  12,400#  per  sq.  in. 

The  maximum  fiber  stress  computed  from  the  assumed  loading  is 
14,945  pounds  per  square  inch,  hence  the  trial  section  is  not  large 
enough  and  a  heavier  section  must  be  tried. 

Properties  of  Column  Sections.  In  the  foregoing  discussion  of 
the  formulas,  it  appears  that  certain  properties  of  the  column  must 
be  known  before  the  formula  can  be  applied.  The  formula  for 
allowable  unit  stress  requires  the  radius  of  gyration  r  and  the 
unsupported  length  /  of  the  column  section.  If  the  column  sup- 
ports an  eccentric  load,  the  moment  of  inertia  7,  or  the  radius 
of  gyration  r,  and  the  distance  to  the  extreme  fiber  c  must  also 
be  known  in  order  to  compute  the  maximum  fiber  stress  due  to 
bending. 

Area.  The  area  A  is  computed  by  adding  together  the  areas 
of  the  several  pieces  which  make  up  the  column  section.  The  areas 
of  the  individual  pieces  are  given  in  the  handbooks.  No  deduction 
is  made  for  rivet  holes. 

Distance  from  Neutral  Axis  to  Extreme  Fiber.  The  distance  to 
the  extreme  fiber  from  the  neutral  axis  is  readily  computed  from  the 
dimensions  of  the  column  section.  It  must  be  taken  from  the  axis 
about  which  the  bending  moment  is  computed.  Thus,  in  Fig. 


182 


STEEL  CONSTRUCTION 


141-b,  C2  must  be  used  in  connection  with  the  load  u,  and  c,  in  con- 
nection with  the  load  v. 

Moment  of  Inertia.  The  moment  of  inertia  is  computed  by  the 
method  explained  and  illustrated  on  p.  37.  It  also  must  be  taken 
in  reference  to  the  neutral  axis  about  which  the  bending  moment  is 
computed.  Thus  in  Fig.  141-b,  7  must  be  calculated  in  reference  to 
axis  2-2  for  the  load  -M,  and  to  axis  1-1  for  the  load  v. 

Radius  of  Gyration.  The  radius  of  gyration  is  computed  about 
each  axis  by  the  method  explained  and  illustrated  on  p.  38.  The 
lesser  value  is  usually  required  for  computing  the  unit  stress,  but 
either  or  both  may  be  required  for  computing  eccentric  effects. 
Thus,  in  Fig.  141-b,  both  radii  of  gyration  are  used. 

There  are  conditions  under  which  the  larger  radius  of  gyration 
is  used.  One  such  case  is  that  of  a  column  built  into  a  masonry 
wall  in  such  a  way  that  it  is  supported  by  the  masonry  in  its  weaker 
direction,  Fig.  142.  Then  the  larger  radius  is  used,  but  designers 
are  cautioned  against  using  this  unless  the  wall  is  so  substantial  that 

it  gives  real  support  to  the  col- 
umn. A  casing  of  brick  or  con- 
crete or  a  poorly  built  brick  wall 
is  not  sufficient. 

It  sometimes  happens  that 
a  column  is  supported  in  one 
direction  at  closer  intervals  than 
in  the  other  direction.  The 
weaker  way  of  the  column  should  be  turned,  if  practicable,  in  the 
direction  of  the  closer  supports.  Then  the  design  may  be  governed 
by  the  lesser  radius  combined  with  the  shorter  length;  or  by  the 
greater  radius  combined  with  the  longer  length. 

Unsupported  Length.  The  length  /  is  needed  for  solving  the 
allowable  unit  stress.  It  is  expressed  in  inches  and  is  the  unsup- 
ported length  of  column.  This  unsupported  length  is  usually 
measured  from  floor  to  floor,  but  if  there  are  deep  girders  with  rigid 
connections,  the  clear  distance  between  girders  may  be  taken  as  the 
length. 

PROBLEM 

Compute  the  values  of  A,  /„  72,  c,,  c2,  rw  and  r2  for  the  column  sections, 
which  are  shown  in  Fig.  143. 


Fig.  142.     Section  Showing  Column  Supported 
by  Masonry  in  Its  Weaker  Direction 


STEEL  CONSTRUCTION 


183 


Column  Sections.  Practically  all  rolled  sections  of  steel  may 
be  used  as  columns  or  struts,  but  only  a  few  of  them  are  economical 
when  used  alone.  Most  columns  are  built  up  of  several  pieces. 
Fig.  144  shows  a  number  of  sections. 

Section  a.  The  tingle  angle  is  not  economical  but  may  be  used 
for  a  light  load.  When  used,  its  radius  of  gyration  must  be  taken 
about  the  diagonal  axis. 

Section  b.  Two  angles  make  a  satisfactory  strut  for  short 
lengths  and  light  loads.  Usually  angles  with  unequal  legs  are  used, 
with  the  long  legs  parallel.  The  radii  about  both  axes  are  nearly 
the  same  for  most  sizes.  The  value  about  the  axis  2-2  can  be 
varied  somewhat  by  the  use  of  fillers  between  the  angles.  Such 
fillers  should  be  Spaced  two  to  three  feet  apart. 


Fie.  143.     Diagrams  for  Estimating  Properties  of  Column  Sections 

Section  c.  The  star  strut  is  made  of  two  angles  with  batten 
plates.  The  batten  plates  in  each  direction  are  spaced  from  two  to 
four  feet  apart.  They  must  be  wide  enough  for  two  rivets  in  each 
end.  The  least  radius  is  about  the  diagonal  axis  3-3.  In  accord- 
ance with  the  rule,  p.  180,  this  being  a  battened  section,  the  unit 
stress  should  be  only  one-half  that  given  by  the  formula.  Conse- 
quently, the  section  is  not  economical  but  is  suitable  to  use  when 
the  load  is  light.  It  is  quite  useful  as  a  brace  between  trusses  .and 
other  similar  situations. 

Section  d.  Four  angles  placed  at  the  corners  of  a  square  and 
joined  together  with  lacing  bars  can  be  made  to  have  a  large  radius 
of  gyration  with  a  small  area.  This  makes  a  column  suitable  for 
supporting  light  loads  on  .a  long  length.  It  is  not  suitable  for 
eccentric  loads.  The  spacing  of  the  angles  may  be  made  as  great 


J/IN          j       i 

(C)  fe=»_l_<=5£j  «5S»__| 

^"/ji 


Fig.  144.     Typical  Column  Sections 


STEEL  CONSTRUCTION  185 

as  required  by  the  conditions.  The  allowable  unit  stress  on  this 
section  must  be  reduced  on  account  of  the  lacing  in  accordance  with 
the  rule,  p.  180.  However,  if  the  column  is  filled  and  encased  in 
concrete,  the  full  unit  stress  may  be  used.  It  is  well  adapted  to 
use  in  this  way.  On  account  of  the  weight  of  the  lacing  and  the 
cost  of  shop  labor,  this  section  is  more  expensive  than  most  others 
for  a  given  area,  hence  it  is  used  only  for  conditions  described 
above. 

Section  e.  When  the  angles  are  placed  in  this  form,  the  cost  of 
shop  work  is  somewhat  reduced,  but  otherwise  the  above  comments 
apply. 

Section  f.  The  Gray  column*  is  made  of  eight  angles  joined 
together  in  pairs  and  these  pairs  are  assembled  into  a  column  by 
means  of  batten  or  tie  plates.  The  batten  plates  are  usually  made 
8"  X  I"  and  spaced  2'-6",  center  to  center  The  advantages  of  this  sec- 
tion are  its  large  radius  of  gyration  and  ease  of  making  connections 
for  beams  and  girders.  Its  disadvantages  are  that  it  is  a  battened 
column  and,  therefore,  not  capable  of  carrying  the  full  unit  stress 
given  by  the  column  formula;  and  thatthe  expense  of  its  manufacture 
is  high,  due  to  the  bent  batten  plates.  It  has  been  used  extensively 
with  the  full  unit  stress;  however,  it  seems  more  reasonable  to  make 
some  reduction.  Since  the  battens  are  quite  rigid  the  column  is 
probably  as  good  as  a  laced  column,  hence  it  can  be  used  with  a 
reduction  of  25  per  cent  from  the  full  unit  stress.  This  column  is  not 
adapted  to  eccentric  loads  and  is  best  suited  to  load  conditions 
which  would  bring  in  equal  loads  to  each  of  its  four  parts.  This 
seldom  occurs,  the  most  common  arrangement  being  two  girders  on 
opposite  sides  and  two  joists  on  the  other  sides.  Thus  two 
segments  of  the  column  are  loaded  much  more  heavily  than  the 
other  two.  The  batten  plates  cannot  be  relied  upon  to  equalize 
the  load,  but 'heavier  angles  can  be  used  for  the  heavier  loads.  If 
this  system  of  proportioning  each  segment  to  suit  the  loads  which 
connect  directly  to  it  is  used,  the  chief  objection  to  this  type  of 
column  is  eliminated. 

When  filled  and  encased  in  concrete,  the  Gray  column  is  very 
rigid  and  can  then  be  loaded  to  the  full  unit  stress.  It  is  especially 
suitable  as  the  core  of  concrete  columns,  and  can  be  used  thus  in 

'Designed  and  patented  by  J.  H.  Gray,  C.  E.,  New  York,  N.  Y. 


186  STEEL  CONSTRUCTION 

connection  with  reinforced  concrete  floor  framing.  When  so  used, 
the  column  may  be  rotated  45  degrees  irom  the  axis  of  the  girders 
if  it  is  desired  to  pass  the  reinforcing  rods  through  the  column. 
The  bearing  of  the  beams  and  girders  in  part  can  be  directly  on  the 
concrete  core  and  in  part  on  lug  angles  riveted  to  the  faces  of  the 
column. 

The  Gray  column  can  be  made  any  desired  size  using  any 
standard  angles.  'The  practicable  limits  are  ten  inches  square 
(minimum)  and  twenty  inches  square  (maximum). 

Sectidn  g.  A  column  made  olfour  angles  laced  has  little  merit  as 
compared  with  the  plate  and  angle  .column  which  is  next  described. 
Its  only  claim  is  that  in  some  cases  it  may.  be  cheaper  to  use  lacing 
than  to  use  a  web  plate.  This  would  be  so  if  there  were  some 
special  condition  requiring  a,  deep  column.  As  with  other  laced 
columns,  it  should  not  be  allowed  the  full  unit  stress  and  should  not 
be  subject  to  any  considerable  eccentricity, 

Section  h.  The  plate  and  angle  column' is  probably  the  most  pop- 
ular shape  for  buildings.  It  does  not  give  the  most  economical  dis- 
tribution of  metal,  as  the  value  of  f  is  much  greater  about  the  axis  1-1 
than  about  2-2.  Its  advantages  are  economy  of  manufacture  and 
ease  of  making  connections.  Advantage  can  be  taken  of  the  greater 
value  of  r  (and  therefore  of  /)  about  the  axis  1-1,  in  providing  for 
eccentric  loads  by  so  placing  the  column  that  the  bending  moment 
is  about  this  axis. 

Sections  i,  j,  and  k.  In  the  use  of  heavy  forms  of  plate  and  angle 
columns,  a  considerable  variation  in  area  can  be  made  by  varying 
the  thickness  of  metal,  keeping  the  depth  constant,  and  making  only 
a  slight  change  in  the  width.  If  greater  area  is  needed,  flange  and 
web  plates  may  be  added  as  in  i,  and  still  greater  area  may  be 
secured  by  using  the  forms ,;  and  k.  Section  k  is  difficult  to  fabricate. 
The  flange  plates  must  be  riveted  to  the  center  web  first,  and  after 
this  is  done  it  is  difficult  to  insert  the  outside  web. 

Section  L  Two  channels  laced  have  a  large  value  of  r  in  propor- 
tion to  the  area.  The  channels  can  be  so  spaced  that  the  values  of 
r  for  both  axes  are  about  equal.  This  section  of  column  has  the 
same  disadvantage's  as  to  unit  stress  and  eccentric  loads  as  other 
laced  columns.  The  connections  for  beams  and  columns  are  more 
difficult  to  make  than  on  plate  and  angle  columns. 


STEEL  CONSTRUCTION  187 

Sections  m,  n,  and  o.  The  columns  made  of  channels  and  plates 
have  good  distribution  of  metal.  Their  chief  disadvantage  is  the 
difficulty  of  making  connections.  All  rivets  in  connections,  except 
those  which  go  through  the  flanges  of  the  channels,  must  be  driven 
before  the  plates  and  channels  are  assembled.  The  section  o,  having 
three  webs,  has  the  same  difficulty  of  fabrication  as  section  k.  Ob- 
jection is  sometimes  made  to  the  closed  box  section;  This  is  dis- 
cussed later. 

Sections  p.  and  q.  Section  p  is  the  standard  Z-bar  column,  and 
section  q  is  the  Z-bar  column  with  flange  plates.  The  distribution 
of  metal  is  not  as  good  as  in  channel  columns  and  the  connections 
are  even  more  difficult.  These  sections  were  formerly  much  used 
but  now  only  rarely. 

Section  r.  The  standard  I-beam  is  not  an  economical  column 
section  but  is  used  to  meet  special  conditions.  It  is  suitable  when 
built  into  a  solid  masonry  wall  with  its  web  perpendicular  to  the 
axis  of  the  wall.  It  is  thus  supported  sidewise  continuously  and 
can  be  designed  in  reference  to  its  larger  radius  of  gyration.  In 
apartment  or  residence  work  it  is  sometimes  so  desirable  to  keep 
the  column  within  the  thickness  of  the  partition  that  the  lack  of 
economy  of  the  I-beam  column  is  justified. 

Sections  s,  t,  w,  and  v.  The  columns  s,  t,  u,  and  v  are  not  much 
used.  There  are  no  serious  objections  to  any  of  them,  and  they  may 
have  advantages  in  special  situations.  Quick  service  from  stock 
material  may  require  the  use  of  tJiese  sections. 

Section  w.  The  Carnegie  \-\-sections  are  designed  especially  for 
use  as  columns.  There  are  only  four  sizes,  viz,  4,  5,  6,  and  8  inches, 
respectively,  and  only  one  weight  for  each  size,  consequently  their 
range  of  usefulness  is  very  limited.  The  radius  of  gyration  about 
the  axis  1-1  is  greater  than  that  about  2-2,  but  the  distribution  of 
metal  is  as  good  as  in  any  H-shaped  column.  They  are  economical 
because  so  little  labor  is  required  for  fabricating  them.  Only  the 
6-inch  and  8-inch  sizes  can  be  used  where  beams  must  be  connected 
to  the  flanges. 

Sections  x  and  y.  The  Bethlehem  columns  have  a  large  range  of 
sizes  and  weights.  If  the  H-section  in  x  is  not  heavy  enough  for  the 
load,  it  can  be  increased  by  riveting  on  flange  plates  as  in  y.  The 
advantage  of  this  type  of  column  is  economy  of  fabrication,  the  only 


188  STEEL  CONSTRUCTION 

riveting  required  being  for  connections,  except  when  flange  plates 
are  used.  A  part  of  this  advantage  is  lost  in  the  heavier  sections 
because  all  holes  must  be  drilled,  due  to  thickness  of  metal.  The 
thick  metal  is  not  as  strong  nor  as  reliable  as  the  thinner  metal  used 
in  built-up  sections. 

Tables.  No  comprehensive  set  of  tables  giving  the  properties 
and  strength  of  columns  has  been  published.  But  there  are  many 
partial  tables  which  are  of  great  assistance  in  designing.  These 
tables  can  be  divided  into  three  classes  as  follows:  (1)  tables  giving 
the  properties  of  the  sections;  (2)  tables  giving  the  values  of  the 

allowable  unit  stresses  for  different  values  of  -;.and  (3)  tables  giving 

strength  of  columns  of  various  sections  and  lengths. 

Properties  of  Sections.  The  properties  of  sections  needed  are 
area  A;  radius  of  gyration  r;  moment  of  inertia  7;  and  distance  to 
extreme  fiber  c.  (See  p.  181).  If  the  column  is  a  single  rolled 
section,  its  properties  can  be  taken  from  the  tables  in  the  handbooks. 
The  values  for  standard  angles  and  I-beams  are  given  in  all  the 
handbooks;  for  the. Carnegie  H-columns,  in  the  Carnegie  Pocket 
Companion,  1913  edition;  and  for  the  Bethlehem  columns,  in  the 
Bethlehem  handbook. 

Built-up  columns  may  be  made  up  in  such  vast  numbers  of 
combinations  that  no  complete  or  very  extensive  tables  have  been 
published.  However,  the  more  common  sizes  are  given  in  some  of 
the  handbooks.  The  area  A  and  the  distance  to  the  extreme  fiber 
c  are  readily  computed  from  the  sizes  of  material  used  in  the  column. 
The  Cambria  and  Carnegie  (1913)  handbooks  give  the  radii  of 
gyration  r  and  the  moments  of  inertia  /  for  laced  channel  columns, 
plate  and  channel  columns,  and  plate  and  angle  columns.  The 
Carnegie  handbook  (1903)  gives  these  properties  for  Z-bar  columns. 
Similar  data  for  about  the  same  range  of  sizes  are  given  in  a  number 
of  other  books  on  steel  construction. 

Allowable  Unit  Stress.  The  allowable  unit  stress  adopted  for 
this  work  has  been  given  and  illustrated  heretofore.  Its  formula  is 

P=  16,000-70- 
r 

This  is  sometimes  known  as  the  American  Railway  Engineers' 
formula  and  is  hereinafter  referred  to  as  the  A.  R.  E.  formula. 


STEEL  CONSTRUCTION  189 

In  the  Carnegie  Pocket  Companion,  (1913  Edition)  pp.  254-5, 
are  shown  a  table  and  a  diagram  which  give  the  values  of  P  as 
determined  from  several  other  formulas.  The  formula  recom- 
mended by  the  American  Bridge  Company  does  not  differ  greatly 
from  the  A.  11.  E.  formula  and  may  be  used  (unless  local  building 
ordinances  require  otherwise). 

The  formula  used  by  the  Bethlehem  Steel  Company  is 

P  =  10,000-55- 
r 

with  a  maximum  value   13,000.     The  resulting  unit  stresses  for 
values  of  —  greater  than  45  are  higher  than  given  by  the  A.  R.  E. 

formula,  and  for  values  of  -  greater  than  G5  are  higher  than  given  by 

the  American  Bridge  Company  formula. 

It  saves  much  time  in  designing  to  have  the  values  of  P  worked 
out  for  the  usual  values  of  I  and  r.  Table  V  gives  the  values  of  P 
for  values  of  r  ranging  from  0.1  inch  to  6.0  inches  and  for  lengths 
ranging  from  3  feet  to  40  feet.  Table  VI  gives  the  values  of  P  for 

values  of  —  ranging  from  30  to  150. 

Strength  of  Columns.  As  indicated  above,  there  has  not  been 
general  agreement  on  the  formula  for  the  allowable  unit  stress, 
consequently  the  tables  of  strength  of  columns- which  have  been 
published  have  been  based  on  several  different  formulas. 

The  Bethlehem  handbook  gives  the  strength  of  Bethlehem  H- 
columns  computed  from  their  formula  given  above.  Table  VII 
gives  the  strengths  of  these  columns  based  on  the  A.  R.  E.  formula, 
f Computed  by  the  Bethlehem  Steel  Company,  for  use  in  Chicago.) 

The  Carnegie  Pocket  Companion  (1913)  gives'  tables  for  Car- 
negie H-columns,  I-beam  columns,  channel  columns,  and  plate  and 
angle  columns,  based  on  the  American  Bridge  Company  formula. 

Table  VIII  gives  the  strengths  of  channel  columns  based  on 
the  A.  R.  E.  formula  (computed  by  the  American  Bridge  Company). 
The  strengths  of  plate  and  angle  columns  based  on  the  A.  R.  E. 
formula  are  given  in  a  pamphlet  "Specifications  for  Steel  Structures" 
(Chicago  Edition),  published  by  the  American  Bridge  Company 
and  distributed  by  its  Chicago  office. 


190 


STEEL  CONSTRUCTION 


TABLE  V 
Unit  Stress  in  Compression  in  Columns 

For  values  of  r  from  0.1  to  6.0  and  lengths  from  3  feet  to  40  feet.  Unit  Stresses 
are  given  in  Thousands  of  Pounds  per  Square  Inch. 

Radius  of 
Gyration 

LENGTH  OF  COLUMN 

3' 

4' 

5' 

6' 

7' 

8' 

9'    |10'  I  IV  |12' 

13'  1  14' 

15' 

16' 

0.1 

0.2 

0.3 

7.6 

0.4 

9.7 

7.6 

5.5 

0.5 

11.0 

9.3 

7.6 

5.9 

0.6 

11.8 

10.4 

9.0 

7.6  1  6.2 

0.7 

12.4 

11.2 

10.0 

8.8 

7.6 

6.4 

0.8 

12.8 

11.8 

10.7 

9.7 

8.6 

7.6 

6.5 

5.5 

0.9 

13.2 

12.3 

11.3 

10.4 

9.5 

8.5 

7.6  1  6.7 

5.7 

1.0 

13.5 

12.6 

11.8 

11.0 

10.1 

9.3 

8.4 

7.6 

6.8 

5.9 

1.1 

13.7 

12.9 

12.2 

11.4 

10.6 

9.9 

9.1 

8.4 

7.6 

6.8 

6.1 

1.2 

13.9 

13.2 

12.5 

11.8 

11.1 

10.4 

9.7 

9.0 

8.3 

7.6  \  6.9 

6.2 

5.5 

1.3 

14.1 

13.4 

12.8 

12.1 

11.5 

10.8 

10.2 

9.5 

8.9 

8.2 

7.6 

6.9 

6.3 

5.7 

1.4 

14.2 

13.6 

13.0 

12.4 

11.8 

11.2 

10.6 

10.0 

9.4 

8.8 

8.2 

7.6 

7.0  |  6.4 

1.5 

14.3 

13.8 

13.2 

12.6 

12.1 

11.5 

11.0 

10.4 

9.8 

9.3 

8.7 

8.2 

7.6 

7.0 

1.6 

14.4 

13.9 

13.4 

12.8 

12.3 

11.8 

11.3 

10.7 

10.2 

9.7 

9.2 

8.6 

8.1 

7.6 

1.7 

14.5 

14.0 

13.5 

13.0 

12.5 

12.0 

11.5 

11.1 

10.6 

10.1 

9.6 

9.1 

8.6 

8.1 

1.8 

14.6 

14.1 

13.7 

13.2 

12.7 

12.3 

11.8 

11.3 

10.9 

10.4 

9.9 

9.5 

9.0 

8.5 

1.9 

14.7 

14.2 

13.8 

13.3 

12.9 

12.5 

12.0 

11.6 

11.1 

10.7 

10.2 

9.8 

9.4 

8.9 

2.0 

14.7 

14.3 

13.9 

13.5 

13.1 

12.6 

12.2 

11.8 

11.4 

11.0 

10.5 

10.1 

9.7 

9.3 

2.1 

14.8 

14.4 

14.0 

13.6 

13.2 

12.8 

12.4 

12.0 

11.6 

11.2 

10.8 

10.4 

10.0 

9.6 

2.2 

14.8 

14.5 

14.1 

13.7 

13.3 

12.9 

12.6 

12.2 

11.8 

11.4 

11.0 

10.6 

10.3 

9.9 

2.3 

14.9 

14.5 

14.2 

13.8 

13.4 

13.1 

12.7 

12.3 

12.0 

11.6 

11.2 

10.9 

10.5 

10.2 

2.4 

14.9 

14.6 

14.2 

13.9 

13.5 

13.2 

12.8 

12.5 

12.1 

11.8 

11.4 

11.1 

10.7 

10.4 

2.5 

15.0 

14.7 

14.3 

14.0 

13.6 

13.3 

13.0 

12.6 

12.3 

12.0 

11.6 

11.3 

11.0 

10.6 

2.6 

15.0 

14.7 

14.4 

14.1 

13.7 

13.4 

13.1 

12.8 

12.4 

12.1 

11.8 

ll.rf 

11.1 

10.8 

2.7 

15.1  [  14.8 

14.4 

14.1 

13.8 

13.5 

13.2 

12.9 

12.6 

12.3 

12.0 

11.6 

11.3 

11.0 

2.8 

15.1 

14.8 

14.5 

14.2 

13.9 

13.6 

13.3 

13.0 

12.7 

12.4 

12,1 

11.8 

11.5 

11.2 

2.9 

15.1 

14.8 

14.5 

14.3 

14.0 

13.7 

13.4 

13.1 

12.8 

12.5 

12.2 

11.9 

11.7 

11.4 

3.0 

15.2 

14.9 

14.6 

14.3 

14.0 

13.8 

13.5 

13.2 

12.9 

12.6 

12.4 

12.1 

11.8 

11.5 

•Sg 

3' 

4' 

5'- 

6' 

7' 

8' 

9' 

10' 

IV 

12' 

13' 

14' 

15' 

16' 

STEEL  CONSTRUCTION 


191 


TABLE  V  (Continued) 

Formula         P=  16,000-  70  - 

in  which             P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches 
1=  length  in  inches 

Unit  stresses  above  the  heavy  zigzag  line  are  values  of  y  from  125  to  150 

LENGTH  OF  COLUMN 

Radius  of 
Gyration 

17' 

IF 

19' 

20' 

21' 

22' 

23' 

24' 

25' 

26' 

27' 

28'  |29' 

30' 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

5.8 

1.4 

65 

5.9 

1.5 

7.1 

6.5 

6.0 

5.5 

1.6 

7.6 

7.1 

6.6 

6.1 

5.6 

1.7 

8.1 

7.6 

7.1 

6.7 

6.2 

5.7 

1.8 

8.5 

8.0 

7.6 

7.2 

6.7 

6.3 

5.8 

1.9 

8.9 

8.4 

8.0 

7.6 

7.2 

6.8 

6.3 

5.9 

5.5 

2.0 

9.2 

8.8 

8.4 

8.0 

7.6 

7.2 

6.8 

6.4 

6.0 

5.6 

2.1 

9.5 

9.1 

8.7 

8.4 

8.0 

7.6 

7.2 

6.8 

6.4 

6.1 

5.7 

2.2 

9.8 

9.4 

9.1 

8.7 

8.3 

8.0 

7.6 

7.2 

6.9 

6.5 

6.1 

5.8 

2.3 

10.0 

9.7 

9.3 

9.0 

8.6 

8.3 

7.9 

7.6 

7.2 

6.9 

6.5 

6.2 

5.8 

5.5 

2.4 

10.3 

9.9 

9.6 

9.3 

8.9 

8.6 

8.3 

7.9 

7.6 

7.3 

6.9 

6.6 

6.3 

5.9 

2.5 

10.5 

10.2 

9.9 

9.5 

9.2 

8.9 

8.6 

8.2 

7.9 

7.6 

7.3 

6.9 

6.6 

6.3 

2.6 

10.7 

10.4 

10.1 

9.8 

9.5 

9.2 

8.8 

8.5 

8.2 

7.9 

7.6 

7.3 

7.0 

6.7 

2.7 

10.9 

10.6 

10.3 

10.0 

9.7 

9.4 

9.1 

8.8 

8.5 

8.2 

7.9 

7.6 

7.3 

7.0 

2.8 

11.1 

10.8 

10.5 

10.2 

9.9 

9.6 

9.3 

9.0 

8.8 

8.5 

8.2 

7.9 

7.6 

7.3 

2.9 

11.2 

11.0 

10.7 

10.4 

10.1 

9.8 

9.6 

9.3 

9.0 

8.7 

8.4 

8.2 

7.9 

7.6 

3.0 

17' 

18' 

19' 

20' 

2V 

22' 

23' 

24' 

25' 

26' 

27' 

28' 

29' 

30' 

•Sg 

192 


STEEL  CONSTRUCTION 


TABLE  V  (Continued) 
Unit  Stress  in  Compression  in  Columns 

For  values  of  r  from  0.1  to  6.0  and  lengths  from  3  feet  to  40  feet.  Unit  Stresses 
are  given  in  Thousands  of  Pounds  per  Square  Inch 

•8g 

LENGTH  OF  COLUMN 

8' 

9' 

10' 

11' 

12'  1  13' 

14' 

15' 

16' 

17'  |  18' 

19' 

20' 

21' 

3.1 

13.8 

13.6 

13.3 

13.0 

12.7  1  12.5 

12.2 

11.9 

11.7 

11.4 

11.1 

10.8 

10.6 

10.3 

3.2 

13.9 

13.6 

13.4 

13.1 

12.8 

12.6 

12.3 

12.1 

11.8 

11.5 

11.3 

11.0 

10.7 

10.5 

3.3 

14.0 

13.7 

13.4 

13.2 

12.9 

12.7 

12.4 

12.2 

11.9 

11.7 

11.4 

11.2 

10.9 

10.6 

3.4 

14.0 

13.8 

13.5 

13.3 

13.0 

12.8 

12.5 

12.3 

12.0 

11.8 

11.5 

11.3 

11.1 

10.8 

3.5 

14.1 

13.8 

13.6 

13.4 

13.1 

12.9 

12.6 

12.4 

12.2 

11.9 

11.7 

11.4 

11.2 

11.0 

3.6 

14.1 

13.9 

13.7 

13.4 

13.2 

13.0 

12.7 

12.5 

12.3 

12.0 

11.8 

11.6 

11.3 

11.1 

3.7 

14.2 

14.0 

13.7 

13.5 

13.3 

13.0 

12.8 

12.6 

12.4 

12.1 

11.9 

11.7 

11.5 

11.2 

3.8 

14.2 

14.0 

13.8 

13.6 

13.3 

13.1 

12.9 

12.7 

12.5 

12.2 

12.0 

11.8 

11.6 

11.4 

3.9 

14.3 

14.1 

13.8 

13.6 

13.4 

13.2 

13.0 

12.8 

12.5 

12.3 

12.1 

11.9 

11.7 

11.5 

4.0 

14.3 

14.1 

13.D 

13.7 

13.5 

13.3 

13.1 

12.8 

12.6 

12.4 

12.2 

12.0 

11.8 

11.6 

4.1 

14.4 

14.2 

13.9 

13.7 

13.5 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.1 

11.9 

11.7 

4.2 

14.4 

14.2 

14.0 

13.$ 

13.6 

13.4 

13.2 

13.0 

12.8 

12.6 

12.4 

12.2 

12.0 

11.8 

4.3 

14.4 

14.2 

14.0 

13.8 

13.6 

13.5 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.1 

11.9 

4.4 

14.5 

14.3 

14.1 

13.9 

13.7 

13.5 

13.3 

13.1 

12.9 

12.8 

12.6 

12.4 

12.2 

12.0 

4.5 

14.5 

14.3 

14.1 

13.9 

13.8 

13.6 

13.4 

13.2 

13.0 

12.8 

12.6 

12.4 

12.3 

12.1 

4.6 

14.5 

14.4 

14.2 

14.0 

13.8 

13.G 

13.4 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.2 

4.7 

14.6 

14.4 

14.2 

14.0 

13.8 

13.7 

13.5 

13.3 

13.1 

13.0 

12.8 

12.6 

12.4 

12.2 

4.8 

14.6 

14.4 

14.2 

14.1 

13.9 

13.7 

13.5 

13.4 

13.2 

13.0 

12.8 

12.7 

12.5 

12.3 

4.9 

14.6 

14.5 

14.3 

14.1 

13.9 

13.8 

13.6 

13.4 

13.3 

13.1 

12.9 

12.7 

12.6 

12.4 

5.0 

14.7 

14.5 

14.3 

14.1 

14.0 

13.8 

13.6 

13.5 

13.3 

13.1 

13.0 

12.8 

12.6  1  12.5 

5.1 

14.7 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.5 

13.4 

13.2 

13.0 

12.9 

12.7  1  12.5. 

5.2 

14.7 

14.5 

14.4 

14.2 

14.1 

13.9 

13.7 

13.6 

13.4 

13.2 

13.1 

12.9 

12.8 

12.6 

5.3 

14.7 

14.6 

14.4 

14.3 

14.1 

13.9 

13.8 

13.6 

13.5 

13.3 

13.1 

13.0 

12.8 

12.7 

5.4 

14.7 

14.6 

14.4 

14.3 

14.1 

14.0 

13.8 

13.7 

13.5 

13.3 

13.2 

13.0 

12.9 

12.7 

5.5 

14.8 

14.6 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.6 

13.4 

13.2 

13.1 

12.9 

12.8 

5.6 

14.8 

14.6 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.6 

13.4 

13.3 

13.1 

13.0 

12.8 

5.7 

14.8 

14.7 

14.5 

14.4 

14.2 

14.1 

13.9 

13.8 

13.6 

13.5 

13.3 

13.2 

13.0 

12.9. 

5.8 

14.8 

14.7 

14.5 

14.4 

14.3 

14.1 

14.0 

13.8 

13.7 

13.5 

13.4 

13.2 

13.1 

13.0 

5.9 

14.9 

14.7 

14.6 

14.4 

14.3 

14.1 

14.0 

13.9 

13.7 

13.6 

13.4 

13.3 

13.1 

13.0 

6.0 

14.9 

14.7 

14.6  1  14.5 

14.3 

14.2 

14.0 

13.9 

13.8 

13.6 

13.5 

13.3 

13.2 

13.1 

|  Radius  of 
I  Gyration 

8' 

9' 

10' 

TV 

12' 

13' 

14' 

15' 

16' 

17; 

18' 

19' 

20' 

21' 

STEEL  CONSTRUCTION 


103 


TABLE  V  (Continued) 

Formula         P=  10,000-70  - 

in  which             P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches. 
1  =  length  in  inches. 

1'nit  stresses  above  the  heavy  zigzag  line  are  values  of  —  from  125  to  150 

LKNGT1I  OF  COLUMN 

1| 

KO 

22'     23' 

24' 

25' 

26' 

27' 

28' 

29' 

30' 

32' 

34' 

36' 

38' 

40' 

1().0|   9.8 

9.5 

9.2 

8.9  |   8.7 

8.4 

8.1 

7.9  1    7.3 

6.8 

6.2 

5.7 

3.1 

10.2 

10.0     97 

9.4  |   9.2 

8.9  |   8.6 

8.4 

8.1 

7.6 

7.1 

6.5 

6.0 

5.5 

3,2 

10.4 

10.  l|   9.9 

9.6 

9.4  |   9.1  1   8.9 

8.6 

8.4 

7.8 

7.3 

6.8  |   6.3 

5.8 

3.3 

10.6 

10.3 

10.1 

9.8 

9.6 

9.3 

9.1 

8.8 

8.6 

8.1 

7.6 

7.1 

6.6 

6.1 

3.4 

10.7 

10.5 

10.2 

10.0 

9.8 

9.5 

9.3 

9.0 

8.8 

8.3 

7.8 

7.4 

6.9 

6.4 

3.5 

10.9 

10.6 

10.4 

10.2 

9.9 

9.7 

9.5 

9.2 

9.0 

8.5 

8.1 

7.6 

7.1 

6.7  1  3.6 

11.0 

10.8  1  10.5  1  10.3 

10.1 

9.9 

9.6 

9.4 

9.2 

8.7 

8.3 

7.8 

7.4 

6.9 

3.7 

11.1  |10.9 

10.7 

10.5 

10.2 

10.0 

9.8 

9.6 

9.4 

8,9 

8.5 

8.0 

7.6 

7.2 

3.8 

11.3|ll.O 

10.8 

10.6 

10.4 

10.2 

10.0 

9.7 

9.5 

9.1 

8.7 

8.2 

7.8 

7.4 

3.9 

11.4  1  11.2 

11.0 

10.7 

10.5 

10.3 

10.1 

9.9 

9.7 

9.3 

8.9 

8.4 

8.0 

7.6 

4.0 

11.5  1  11.3 

11.1 

10.9 

10.7 

10.5 

10.3 

10.1 

9.8 

9.4 

9.0 

8.6 

8.2 

7.8 

4.1 

11.6 

11.4 

11.2  |  ll.0|  10.8  1  10.6  1  10.4 

10.2  1  10.0 

9.6 

9.2 

8.8  |   8.4 

8.0 

4.2 

11.7 

11.5 

11.3|ll.l 

10.9  1  10.7  1  10.5  1  10.3  1  10.1  1   9.7  |   9.4 

9.0  |   8.6 

8.2 

4.3 

11.8 

J1.6 

11.4  1  11.2 

11.0|l0.8 

10.7  1  10.5  1  10.3  |   9.9  |   9.5 

9.l|   8.7 

8.4 

4.4 

11.9 

11.7 

11.5 

11.3 

11.1 

11.0 

10.8 

10.6 

10.4 

10.0 

9.6 

9.3 

8.9 

8.5 

4.5 

12.0 

11.8 

11.6 

11.4 

11.2 

11.1 

10.9 

10.7 

10.5 

10.2 

9.8 

9.4 

9.1 

8.7 

4.6 

12.1 

11.9  1  11.7 

11.5 

11.3 

11.2 

11.0 

10.8 

10.6  1  10.3 

9.9 

9.6 

9.2 

8.8  1  4.7 

12.l|l20 

11.8 

11.6  1  11.4 

11.3  1  11.1  1  10.9 

10.7  1  10.4 

10.0  |   9.7 

9.3 

9.0 

4.8 

12.2 

12.1 

11.9 

11.7  1  11.5 

11.4  1  11.2 

11.0  1  10.9  1  10.5 

10.2  |   9.8 

9.5 

9.1 

4.9 

12.3 

12.1 

12.0 

11.8 

11.6 

11.5 

11.3 

11.1 

11.0 

10.6 

10.3 

9.9 

9.6 

9.3 

5.0 

12.4 

12.2 

120 

11.9 

11.7 

11.5 

11.4 

11.2 

11.1 

10.7 

10.4 

10.1 

9.7 

9.4 

5.1 

12.4 

12.3 

12.1 

12.0 

11.8 

11.6 

11.5 

11.3 

11.1 

10.8 

10.5 

10.2  |   9.9 

9.5 

5.2 

12.5  1  12.3 

12.2 

12.0  |l  1.9 

11.7  1  11.6 

11.4 

11.2 

10.9 

10.6 

10.3 

10.0 

9.7 

5.3 

12.6 

12.4 

12.3 

12.1  1  11.9  1  11.8  1  11.6 

11.5  1  11.3  1  11.0  1  10.7 

10.4 

10.1 

9.8 

5.4 

12.6 

12.5 

12.3 

12.2 

12.0 

11.9 

11.7 

11.6 

11.4 

11.1 

10.8 

10.5 

10.2 

9.9 

5.5 

12.7 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.6 

11.5 

11.2 

10.9 

10.6 

10.3 

10.0 

5.6 

12.8 

12.6 

12.5 

12.3 

12.2 

12.0 

11.9 

11.7 

11.6 

11.3 

11.0  1  10.7 

10.4 

10.1 

5.7 

12.8 

12.7 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.6 

11.4 

11.  l|  10.8 

10.5 

10.2 

5.8 

12.9 

12.7 

12.6 

12.4 

12.3 

12.2  1  12.0 

11.9 

11.7 

11.4 

11.2 

10.9  1  10.6 

10.3 

5.9 

12.9 

12.8 

12.6 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.5 

11.2 

11.0 

10.7 

10.4 

6.0 

22' 

23' 

24' 

25' 

26' 

27' 

28' 

29' 

30' 

32' 

34' 

36' 

38' 

40' 

1  Radius  of 
Gyration 

194 


STEEL  CONSTRUCTION 


TABLE  VI 
Unit. Stress  in  Compression 

Values  of  P  for  values  of  -  =  30  to  -  =  150  from  the  formula  P=  16,000-70  - 


I 

r 

16,000-70- 
14.000  max. 

jt 

r 

16,000-70^ 
14,000  max. 

30 

-  13900 

105 

8650 

35 

13550 

110 

8300 

40 

13200 

115 

7950 

45 

12850 

120 

7600 

50 

12500 

125 

7250 

55 

12150 

130 

6900 

60 

11800 

135 

6550 

65 

11450 

140 

6200 

70 

11100 

145 

5850 

75 

10750 

150 

5500 

80 

10400 

85 

10050 

90 

9700 

95 

9350 

100 

9000 

It  must  be  noted  that  the  tables  of  strength  of  columns  take  no 
account  of  eccentricity.  If  there  are  eccentric  loads,  the  equivalent 
concentric  loads  must  be  computed  by  the  method  given  on  p.  178, 
and  then  these  values  added  to  the  actual  loads.  This  result  gives 
the  total  load  to  be  used  in  selecting  the  column  section  from  the 
tables. 

Use  of  the  Tables.  The  following  illustrations  show  the  manner 
of  using  the  tables: 

(1)  Assume  a  concentric  load  of  492,000  pounds  on  a  column 
12  feet  long.  Determine  the  required  column  sections  made  of  plates 
and  channels  and  of  plates  and  angles.  Compare  the  areas  of  the 
two  columns. 

(a)     From  Table  VIII,  the  channel  column  section  required  is 

2  L  12"X30" 


Area  =  36.9  sq.  in. 


STEEL  CONSTRUCTION  195 


(b)     From  the  table  of  plate  and  angle  columns  (see  handbook), 
the  angle  column  section  required  is 

1  PI.  12"  XT 
4Ls6"x4"xr 

2  PI.  14"  Xf 
Area  =  39.0  sq.  in. 

In  both  cases  other  sections  might  be  selected. 

(2)  Assume  a  load  of  640,000  pounds  on  a  column  16  feet  long; 
80,000  pounds  of  the  load  has  an  eccentricity  of  9  inches  in  the  direc«- 
tion  of  the  greatest  radius  of  gyration.  Determine  the  plate  and 
angle  column  required,  using  the  A.  R.  E.  formula. 

A  preliminary  selection  from  the  table  indicates  a  column  whose 
greatest  r  is  about  6.8  inches  and  whose  c  is  about  8J  inches.  From 
these  approximate  values  the  concentric  equivalent  load  is 


This  added  to  the  direct  load  gives  a  total  of  739,000  pounds.  The 
column  section  required  is 

1  PL  14"  Xf" 
4Ls6"X4"Xf 

2  PL  14"  XI  A' 

The  values  of  r  and  c  for  this  section  are  6.83  inches  and  8  A  inches, 
so  the  approximate  values  of  r  and  c  used  above  are  accurate 
enough,  hence  no  corrections  need  be  made. 

(3)  Assume  a  column  which  has  an  unsupported  length  of  10 
feet  6  inches  in  its  weaker  direction  and  18  feet  in  its  stronger  direc- 
tion made  of 

1  PL  12"X|" 
4Ls  6"X4"Xf 

Determine  the  allowable  unit  stress. 

From  the  table  the  values  of  r  are  2.69  and  4.91.    The  cor- 

responding values  of  /  are  126  inches  and  216  inches;  and  of—  are 

43  and  44.  The  respective  unit  stresses  are  taken  from  Table  VI  by 
interpolating  between  the  values  for  40  and  45,  giving  13,590  and 
13,720.  The  smaller  value  must  be  used. 


196 


STEEL  CONSTRUCTION 


'» 

* 
1  ,  . 

TABLE  VH 
Safe  Loads  on   Bethlehem   Columns 
14*  H  -Section  with  Cover  Plates 

Safe  Loads  are  given  in  Thousands  of  Pounds 

Lg 

'1-  c—^ 

Weight 
Section 
Lb. 
per  Ft. 

Dimensions,  in. 

Ares  of 
Section 
Square 
Inches 

Least 
Radius 
of  Qyr.. 

Inch* 

UNSUPPORTED  LENGTH 

c 

P 

H 

10 

11 

11 

13 

14 

15 

284.0 

16 

IK 

16% 

83.52 

3.98 

1160.0 

1142.4 

1124.8 

1107.2 

1089.6 

1072.0 

290.8 

16 

lA 

16^ 

85.52 

3.99 

1188.2 

1170.2 

1152.2 

1134.2 

1116.2 

1098.2 

297.6 

16 

1H 

16% 

87.52 

4.01 

1217.0 

1198.6 

1180.4 

1162.0 

1143.6 

1125.4 

304.4 
311.2 

16 
16 

lA 
1% 

17 
17% 

89.52 
9L52 

4.02 
4.04 

1245.2 
1274.0 

1226.6 
1255.0 

1207.8 
1236.0 

1189.2 
1207.0 

1170.4 
1198.0 

1151.8 
1178.8 

318.0 

16 

lA 

17% 

93.52 

4.05 

1302.4 

1283.0 

1263.6 

1244.2 

1224.8 

1205.4 

324.8 

16 

1H 

17% 

95.52 

4.06 

1330.6 

1311.0 

1291.2 

1271.4 

1251.6 

1231.8 

331.6 

16 

1H 

17% 

97.52 

4.08 

1359.6 

1339.4 

1319.4 

1299.4 

1279.2 

1259.2 

338.4 

16 

l% 

17% 

99.52 

4.09 

1388.0 

1367.4 

1347.0 

1326.6 

1306.2 

1285.8 

345.2 

16 

itt 

17H 

101.52 

4.10 

1416.4 

1395.6 

1374.8 

1354.0 

1333.2 

1312.4 

350.3 

17 

IK 

17% 

103.02 

4.30 

1447.0 

1427.0 

1406.8 

1388.6 

1366.6 

1346.4 

357.5 

17 

iH 

1754 

105.15 

4.31 

1477.4 

1457.0 

1436.4 

1416.0 

1395.4 

1375.0 

364.7 

17 

1% 

17% 

107.27 

4.32 

1507.8 

1486.0 

1466.0 

1445.2 

1424.4 

1403.4 

372.0 

17 

iH 

18 

109.40 

4.33 

1538.2 

1517.0 

1495.8 

1474.6 

1453.2 

1432.0 

379.2 

17 

2 

18% 

111.52 

4.35 

1569.0 

1547.4 

1526.0 

1504.4 

1482.8 

1461.2 

386.4 

17 

2A 

18% 

113.65 

4.36 

1599.4 

1577.6 

1555.6 

1533.8 

1511.8 

1490.0 

393.6 

17 

2% 

18% 

115.72 

4.37 

1629.8 

1607.6 

1585.2 

1563.0 

1440.8 

1518.6 

400.9 

17 

2A 

18% 

117.90 

4.38 

1660.2 

1637.6 

1615.0 

1592.4 

1569.8 

1547.2 

408.1 

17 

2% 

18% 

120.02 

4.39 

1690.6 

1667.8 

1644.8 

1621.8 

1598.8 

1575.8 

415.3 

17 

2A 

18H 

122.15 

4.40 

1721.2 

1697.8 

1674.6 

1651.2 

1628.0 

1604.6 

423.4 

18 

2K 

18% 

124.52 

4.62 

1766.0 

1743.2 

1720.6 

1698.0 

1675.4 

1652.8 

431.0 

18 

2A 

18H 

126.77 

4.63 

1798.4 

1775.4 

1752.4 

1729.4 

1706.4 

1683.4 

438.7 

18 

23/8 

18% 

129.02 

4.64 

1830.8 

1807.4 

1784.0 

1?60.6 

1737.4 

1714.0 

446.3 

18 

2A 

19 

131.27 

4.65 

1863.2 

1839.4 

1814.8 

1792.0 

1768.4 

1744.6 

454.0 

18 

2% 

19% 

133.52 

4.66 

1895.6 

1871.6 

1847.6 

1823.4 

1799.4 

1775.4 

461.6 

18 

2A 

19% 

135.77 

4.67 

1928.2 

1903.6 

1879.2 

1854.8 

1830.4 

1806.0 

469.3 

18 

2^8 

19% 

138.02 

4.68 

1960.6 

1935.8 

1911.0 

1886.2 

1861.6 

1836.8 

476.9 

18 

2H 

19% 

140.27 

4.69 

1993.0 

1968.0 

1942.8 

1917.8 

1892.6 

1867.4 

484.6 

18 

254 

19^ 

142.52 

4.70 

2025.6 

2000.2 

1974.6 

1949.2 

1923.8 

189  8.2 

Columns  composed  of  a  14'X148#  Special  Column  Section  (H14b)  reenforced  with 
cover  plates  of  width  and  thickness  given  in  table. 

STEEL  CONSTRUCTION 


197 


TABLE  VII  (Continued) 
I                                       I  jj  r 

Formula      P=  16,000-70^                                        '  JTJJT"1 

in  which      P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches* 

1  =  length  in  inches 

To  the  left  of  heavy  line  values  of  -  do  not  exceed  120 

T                                                                          1*  o  "    '  "I 

OF  COLUMNS  IN  FEET 

We,ght 

16 

18 

20 

22 

24 

28 

32 

36 

40 

Section 
Lb. 
per  Ft. 

1054.2 

1019.0 

983.8 

948.6 

913.2 

842.8 

772.2 

701.8 

631.2 

284.0 

1080.2 

1044.2 

1008.2 

972.2 

936.2 

864.2 

792.2 

720.2 

648.2 

290.8 

1107.0 

1070.4 

1033.6 

997.0 

960.4 

887.0 

813.6 

740.4 

667.0 

297.6 

1133.0 

1095.6 

1058.2 

1020.8 

983.4 

908,6 

833.8 

759.0 

684.0 

304.4 

1159.8 

1121.8 

1083.8 

1045.6 

1007.6 

931.6 

855.4 

779.2 

703.2 

311.2 

1186.0 

1147.2 

1108.4 

1069.6 

1030.8 

953.2 

875.6 

798.0 

720.4 

318.0 

1212.2 

1172.6 

1133.0 

1093.6 

1054.0 

975.0 

896.0 

816.8 

737.8 

324.8 

1239.0 

1199.0 

1158.8 

1118.6 

1078.4 

998.2 

917.8 

837.6 

757.2 

331.6 

1265.2 

1225.4 

1183.6 

1142.6 

1101.8 

1020.0 

938.2 

856.6 

774.8 

338.4 

1291.6 

1250.0 

1208.4 

1166.8 

1125.2 

1042.0 

958.8 

875.6 

792.4 

345.2 

1326.4 

1286.0 

1245.8 

1205.6 

1165.4 

1084.8 

1004.4 

923.8 

843.4 

350.3 

1354.6 

1313.6 

1272.6 

1231.6 

1190.6 

1  108.6 

1026.6 

944.6 

862.6 

357.5 

1382.6 

1340.8 

1299.2 

1257.4 

1215.8 

1132.2 

1048.8 

965.4 

882.0 

364.7 

1410.8 

1368.4 

1326.0 

1283.4 

1241.0 

1156.2 

1071.2 

986.4 

901.4 

372.0 

1439.8 

1396.6 

1353.6 

1310.6 

1267.4 

1181.4 

1095.2 

1009.0 

923.0 

379.2 

1468.0 

1424.2 

1380.4 

1336.6 

1292.8 

1205.4 

1117.8 

1030.2 

942.6 

386.4 

1496.2 

1451.8 

1407.2 

1362.8 

1318.2 

1229.2 

1140.2 

1051.2 

962.2 

393.6 

1524.6 

1479.4 

1434.2 

1389.0 

1343.8 

1253.2 

1162.8 

1072.4 

982.0 

400.9 

1552.8 

1507.0 

1461.0 

1415.0 

1369.2 

1277.2 

1185.4 

1093.6 

1001.8 

408.1 

1581.2 

1534.6 

1488.0 

1441.4 

1394.8 

1301.4 

1208.2 

1115.0 

1021.6 

415.3 

1630.0 

1584.8 

1539.6 

1494.2 

1449.0 

1358.4 

1267.8 

1177.2 

1086.8 

423.4 

1660.4 

1614.4 

1568.4 

1522.4 

1476.4 

1384.4 

1292.4 

1200.4 

1108.4 

431.0 

1690.6 

1643.8 

1597.2 

1550.4 

1503.8 

1410.4 

1316.8 

1223.4 

1130.0 

438.7 

1721.0 

1673.4 

1626.0 

1578.6 

1531.2 

1436.4 

1341.4 

1246.6 

1151.8 

446.3 

1751.2 

1703.0 

1655.0 

1606.8 

1558.6 

1462.4 

1366.2 

1269.8 

1173.6 

454.0 

1781.6 

1732.8 

1683.8 

1635.0 

1586:2 

1488.6 

1390.8 

1293.2 

1195.4 

461.6 

1812.0 

1762.4 

1712.8 

1663.4 

1613.8 

1514.6 

1415.6 

1316.4 

1217.4 

469.3 

1842.4 

1792.2 

1741.8 

1691.6 

1641.4 

1540.8 

1440.4 

1339.8 

1239.4 

476.9 

1872.8 

1821.8 

1770.8 

1720.0 

1669.0 

1567.0 

1465.2 

1363.4 

1261.4 

484.6 

198 


STEEL  CONSTRUCTION 


r-.         *  . 

TABLE  VII  (Continued) 
Safe  Loads  on  Bethlehem  Columns 

t^ 

J 

^ 

14*  H-Section 

Safe  lo  ads  are  given  in  Thousands  of  Pounds 

C—  *_i 

Section 
Number 

Weight 
Section 
Lb. 
per  Ft. 

Dimensions.  Inches 

Least 
Radius 
of  Gyr.. 
Inches 

UNSUPPORTED  LENGTH 

D 

T 

B 

Area  of 
Section 
Sq.  In. 

10 

11 

12 

13 

14 

83.5 

13% 

H 

13.92 

24.46 

3.47 

332.2 

326.2 

320.4 

314.4 

308.4 

91.0 

13% 

% 

13.96 

26.76 

3.49 

363'.8 

357.4 

350.8 

344.4 

338.0 

99.0 

14 

H 

14.00 

29.06 

3.50 

395.2 

388.2 

381.2 

374.2 

367.4 

106.5 

14% 

% 

14.04 

31.38 

3.52 

427.2 

419.8 

412.2 

404.8 

397.2 

114.5 

14J4 

H 

14.08 

33.70 

3.53 

459.0 

451.0 

443.0 

435.0 

427.0 

122.5 

14% 

i 

14.12 

36.04 

3.55 

491.4 

482.8 

474.4 

465.8 

457.2 

;  130.5 

14% 

io 

14.16 

38.38 

3.56 

523.6 

514.4 

505.4 

496.4 

487.2 

138.0 

14% 

1% 

14.19 

40.59 

3.58 

554.2 

544.6 

535.2 

525.6 

516.2 

. 

146.0 

14% 

1A 

14.23 

42.95 

3.59 

586.8 

576.6 

566.6 

556.6 

546.6 

154.0 

14% 

1% 

14.27 

45.33 

3.61 

619.8 

609.2 

598.8 

588.2 

577.6 

162.0 

15 

l^ 

14.31 

47.71 

3.62 

652.6 

641.6 

630.6 

619.4 

608.4 

170.5 

15% 

1% 

14.35 

50.11 

3.64 

686.2 

674.6 

663.0 

651.4 

639.8 

178.5 

15% 

1A 

14.39 

52.51 

3.65 

719.4 

707.2 

695.2 

683.0 

671.0 

H14 

186.5 

15% 

1% 

14.43 

54.92 

3.66 

752.6 

740.0 

727.4 

714.8 

702.2 

195.0 

15H 

lA 

14.47 

57.35 

3.68 

786.6 

773.6 

760.6 

747.4 

734.4 

203.5 

15% 

1% 

14.51 

59.78 

3.69 

820.4 

806.8 

793.2 

779.6 

766.0 

211.0 

15% 

1H 

14.54 

62.07 

3.70 

852.2 

838.2 

824.0 

810.0 

795.8 

219.5 

15% 

1% 

14.58 

64.52 

3.71 

886.2 

871.6 

857.0 

842.4 

827.8 

227.5 

16 

1H 

14.62 

66.98 

3.72 

920.4 

905.4 

890.2 

875.0 

860.0 

236.0 

16% 

1% 

14.66 

69.45 

3.74 

955.2 

939.6 

924.0 

908.4 

892.8 

244.5 

16% 

itt 

14.70 

71.94 

3.75 

989.8 

973.8 

957.6 

941.6 

925.4 

253.0 

16% 

2 

14.74 

74.43 

3.76 

1024.6 

1008.0 

991.4 

974.8 

958.0 

261.5 

16% 

2A 

14.78 

76.93 

3.77 

1059.4 

1042.4 

1025.2 

1008.0 

991.0 

270.0 

16% 

2H 

14.82 

79.44 

3.79 

1095.0 

1077,4 

1059.8 

1042.2 

1024.6 

278.5 

16% 

2A 

14.86 

81.97 

3.80 

1130.4 

1112.2 

1094.0 

1076.0 

1057.8 

287.5 

16% 

2% 

14.90 

84.50 

3.81 

1165.8 

1  147.0 

1128.4 

1109.8 

1091.2 

STEEL  CONSTRUCTION 


199 


TABLE  VII  (Continued) 

Formula  P  =16,000-  70- 
r 
in  which     F  =  unit  stress  in  pounds  per  square  inch 
T  =  radius  of  gyration  in  inches 
/  =  length  in  inches 

To  the  left  of  heavy  line  values  of.-  do  not  exceed  120 

1 

L 

T 
1  ° 

( 

I—  .-.  \ 

OF  COLUMNS  IN  FEET 

Weight 
Section 
Lb. 
per  Ft. 

15 

16 

18 

20 

22 

24 

28 

32 

36 

40 

302.6 

296.6 

284.8 

273.0 

261.0 

249.2 

225.6 

201.8 

178.2 

154.6 

83.5 

331.6 

325.2 

312.2 

299.4 

286.4 

273.6 

247.8 

222.0 

196.2 

170.6 

9J.O 

380.4 

353.4 

339.4 

325.4 

311.6 

297.6 

269.6 

241.8 

213.8 

186.0 

99.0 

389.8 

382.2 

367.2 

352.4 

337.4 

322.4 

292.4 

262.4 

232.4 

202.6 

106.5 

419.0 

410.8 

394.8 

378.8 

362.8 

346.8 

314.6 

282.6 

250.4 

218.4 

114.5 

448.8 

440.2 

423.2 

406.0 

389.0 

372.0 

337.8 

303.8 

269.6 

235.6 

122.5 

478.2 

469.2 

451.0 

433.0 

414.8 

396.8 

360.6 

324.2 

288.0 

251.8 

130.5 

506.6 

497.0 

478.0 

459.0 

440.0 

420.8 

382.8 

344.6 

306.6 

268.4 

138.0 

536.4 
567.0 

526.4 
556.6 

506.2 
535.4 

486.2 
514.4 

466.2 
493.2 

446.0 
472.2 

405.8 
430.0 

365.6 
387.8 

325.4 

285.2 
303.4 

146.0 
154.0 

345.6 

597.2 

586.2 

564.0 

542.0 

519.8 

497.6 

453.4 

409.0 

364.8 

320.6 

162.0 

628.4 

616.8 

593.6 

570.4 

547.4 

524.2 

478.0 

431.8 

385.4 

339.2 

170.5 

658.8 

646.8 

622.6 

598.4 

574.4 

550.2 

501.8 

453.4 

405.2 

356.8 

178.5 

689.6 

677.0 

651.8 

626.6 

601.4 

576.2 

525.8 

475.4 

425.0 

374.6 

186.5 

721.2 

708.2 

682.0 

655.8 

62S.6 

603.4 

551.0 

498.6 

446.4 

394.0 

195.0 

752.4 

738.8 

711.6 

684.4 

657.0 

629.8 

575.4 

521.0 

466.6 

412.2 

203.5 

781.8 

767.6 

739.4 

711.2 

683.2 

655.0 

598.6 

542.2 

485.8 

429.4 

211.0 

813.2 

798.6 

769.4 

740.2 

711.0 

681.8 

623.2 

564.8 

506.4 

448.0 

219.5 

844.8 

829.6 

799.4 

769.2 

739.0 

708.6 

648.2 

587.6 

527.2 

466.8 

227.5 

877.2 

861.6 

830.4 

799.2 

768.0 

736.8 

674.4 

612.0 

549.6 

487.2 

236.0 

909.4 

893.2 

861.0 

828.8 

796.6 

764.2 

699.8 

635.4 

570.8 

506.4 

244.5 

941.4 

924.8 

891.6 

858.4 

825.0 

791.8 

725.2 

658.8 

592.2 

525.8 

253.0 

973.8 

956.6 

922.4 

888.0 

853.8 

819.4 

751.0 

682.4 

613.8 

545.2 

261.5 

1007.0 

989.4 

954.2 

919.0 

8S3.6 

848.4 

778.0 

707.6 

637.2 

566.8 

270.0 

1039.8 

1021.6 

985.4 

949.2 

912.8 

876.6 

804.2 

731.6 

659.2 

586.8 

278.5 

1072.6 

1054.0 

1016.6 

979.4 

942.2 

904.8 

830.4 

755.8 

681.4 

606.8 

287.5 

200 


STEEL  CONSTRUCTION 


a 

TABLE  VII  (Continued) 
Safe  Loads  on  Bethlehem  Columns 
12'  H-Section 

Safe  loads  are  given  in  Thousands  of  Pounds 

2 

u* 

C) 

1 

L—  .-4 

Section 
Number 

Weight 
Section 
Lb. 
per  Foot 

Dimension.  Inches 

Area  of 

Section 
Sq.ln. 

Least 

Radius 
ofGyr. 

Inches 

UNSUPPORTED  LENGTH 

D 

T 

B 

10 

11 

12 

13 

14 

64.5 

HH 

H 

11.92 

19.00 

2.98 

250.4 

245.0 

239.8 

234.4 

229.0 

71.5 

Mi 

H 

11.96 

20.96 

3.00 

276.6 

270.8 

265.0 

259.0 

253.2 

78.0 

12 

H 

12.00 

22.94 

3.01 

303.0 

296.6 

290.2 

283.8 

277.4 

84.5 

I2H 

H 

12.04 

24.92 

3.03 

329.6 

322.8 

315.8 

309.0 

302.0 

91.5 

12K 

H 

12.08 

26.92 

3.04 

356.4 

348.8 

341.4 

334.0 

326.6 

98.5 

12H 

H 

12.12 

28.92 

3.06 

383.4 

375.4 

367.4 

359.6 

351.6 

105.0 

12H 

i 

12.16 

30.94 

3.07 

410.4 

402.0 

393.4 

385.0 

376.6 

H12 

112.0 

«H 

lA 

12.20 

32.96 

3.08 

437.4 

428.4 

419.4 

410.6 

401.6 

118.5 

12H 

IK 

12.23 

34.87 

3.10 

463.4 

454.0 

444.6 

435.0 

425.6 

125.5 

12% 

lA 

12.27 

36.91 

3.11 

490.8 

480.8 

471.0 

461.0 

451.0 

132.5 

13 

IK 

12.31 

38.97 

3.13 

519.0 

508.4 

498.0 

487.6 

477.2 

139.5 

13K 

ift 

12.35 

41.03 

3.14 

546.8 

535.8 

524.8 

513.8 

502.8 

146.5 

13K 

IK 

12.39 

43.10 

3.15 

574.6 

563.2 

551.6 

540.2 

528.6 

153.5 

13H 

1A 

12.43 

45.19 

3.16 

603.0 

591.0 

578.8 

566.8 

554.8 

161.0 

13M 

IK 

12.47 

47.28 

3.18 

631.6 

619.2 

606.6 

594.2 

581.6 

STEEL  CONSTRUCTION 


201 


TABLE  VII   (Continued)                                                     i 

Formula  P  =  16,000-70y 

j 

k1 

in  which     P  =  unit  stress  in  pounds  p<>r  square  inches 
r  =  radius  of  gyration  in  inches 
1  =  length  in  inches 

\    - 

t 

To  the  left  of  heavy  line  values  of  -  do  not  exceed  120             »*         B      "* 

OF  COLUMNS  IN  FEET 

Weight 

15 

16 

18 

20 

22 

24 

28 

32 

36 

Lb. 
per  Foot 

223.6 

218.4 

207.6 

106.8 

186.2 

165.4 

154.0 

132.6 

111.2 

64.5 

247.4 

241.4 

220.8 

218.0 

206.2 

104.6 

171.0 

1476 

124.0 

7*1.5 

271.0 

264.6 

251.S 

230.0 

226.2 

213.4 

187.8 

162.2 

136.6 

78.0 

205.0 

2SS.2 

274.4 

260.0 

246.8 

233.0 

205.2 

177.6 

150.0 

84.5 

310.2 

311.* 

206.8 

282.0 

267.0 

<•)•,••>  o 

222.4 

102.6 

163.0 

01.5 

343.6 

335.6 

310.8 

304.0 

28S.O 

070  o 

240.4 

208.6 

177.0 

08.5 

3G8.0 

350.G 

342.6 

325.8 

308.8 

291.8 

258.0 

224,2 

100.2 

105.0 

302.6 

3S3.6 

365.6 

347.6 

320.6 

311.6 

.375.6 

230.8 

203.8 

112.0 

416.2 

406.8 

387.  S 

360.0 

350.0 

331.2 

203.4 

255.6 

217.8 

118.5 

441.0 

431.0 

411.2 

301.2 

371.2 

351.2 

311.4 

271.6 

231.6 

125.5 

466.C 

456.2 

435.2 

414.4 

303.4 

372.6 

330.6 

288.8 

247.0 

132.5 

401.8 

4SO.S 

450.0 

437.0 

415.0 

303.0 

340.2 

305.2 

261.4 

130.5 

517.2 

505.S 

482.8 

450.8 

436.8 

413.8 

367.8 

321.8 

275.8 

146.5 

542.8 

530.8 

506.8 

482.8 

458.8 

434.8 

386.6 

338.6 

200.6 

153.5 

569.2 

556.6 

531.6 

506.6 

481.8 

456.8 

406.8 

356.8 

306.8 

161.0 

202 


STEEL  CONSTRUCTION 


i 

T                               TABLE  VII  (Continued) 

L                     r*1  -1 

F 

Safe  Loads  on  Bethlehem  Columns 

c 

10"  H-Section 

( 

Safe  loads  are  given  in  Thousands  of  Pounds 

t  .—  | 

Weight 

Dimensions.  Inches 

Area  of 

Least 

UNSUPPORTED  LENGTH 

Section 
Number 

Section 
Lb. 
per  Ft. 

D 

T 

B 

Square 
Inches 

of  Gyr. 
Inches 

10 

11 

12 

13 

14 

49.0 

« 

A 

9.97 

14.37 

2.49 

181.4 

176.6 

171.8 

167.0 

162.0 

54.0 

10 

H 

10.00 

15.91 

2.51 

201.4 

196*0 

190.6 

185.4 

180.0 

59.5 

IQK 

H 

10.04 

17.57 

2.53 

222.8 

217.0 

211.2 

205.2 

199.4 

65.5 

10* 

H 

10.08 

19.23 

2.54 

244.0 

237.8 

231.4 

225.0 

218.6 

71.0 

10H 

H 

10.12 

20.91 

2.56 

266.0 

259.0 

252.2 

245.4 

238.6 

77.0 

10H 

K 

•  10.16 

22.59 

2.57 

287.6 

280.2 

272.8 

265.4 

258.0 

82.5 

10M 

H 

10.20 

24.29 

2.58 

309.6 

301.6 

293.8 

285.8 

278.0 

88.5 

WK 

i 

10.24 

25.99 

2.60 

331.8 

323.4 

315.0 

306.6 

298.2 

H10 

94.0 

IOK 

IA 

10.28 

27.71 

2.61 

354.2 

345.2 

336.4 

327.4 

318.6 

99.5 

11 

iK 

10.31 

29.32 

2.62 

375.2 

365.8 

356.4 

347.0 

337.6 

105.5 

UK 

IA 

10.35 

31.06 

2.64 

398.2 

388.2 

378.4 

368.4 

358.6 

111.5 

UK 

IK 

10.39 

32.80 

2.65 

420.8 

410.4 

400.0 

389.6 

379.2 

117.5 

UN 

lA 

10.43 

34.55 

2.66 

443.6 

432.8 

421.8 

411.0 

400.0 

123.5 

10.47 

36.32 

2.67 

466.8 

455.4 

444.0 

432.6 

421.2 

STEEL  CONSTRUCTION 


203 


TABLE  VII  r  Continued}                                          ,                ,4 

i                                            *  \r-fTJ 
Formula  P=  16,000-70^                                                \\^ 

in  which     P=unit  stress  in  pounds  per  square  inch                                               <* 
r=  radius  of  gyration  in  inches 
1  =  length  in  inches                                                                f~,     ..__,,) 

; 
To  the  left  of  heavy  line  values  of  —  do  not  exceed  120                             a  — 

OF  COLUMNS  IN  FEET 

WeiKht 

15 

16 

18 

20 

22 

24 

26 

28 

30 

Lb. 
per  Ft. 

157.2 

152.4 

142.6 

133.0 

123.2 

113.6 

103.8 

94  J2 

84.4 

49.0 

174.6 

169.4 

158.8 

148.0 

137.4 

126.8 

116.2 

105.4 

94.8 

54.0 

103.6 

187.8 

176.2 

164.4 

152.8 

141.2 

129.4 

117.8 

106.2 

59.5 

212.2 

206.0 

193.2 

180.4 

167.8 

155.0 

142.4 

129.6 

116.8 

65.5 

231.6 

224.8 

211.0 

197.4 

183.6 

169.8 

156.2 

142.4 

128.8 

71.0 

250.6 

243.4 

228.6 

213.8 

199.0 

184.2 

169.4 

154.8 

140.0 

77.0 

270.0 

262.2 

246.2 

230.4 

214.6 

198.8 

183.0 

167.2 

151.4 

82.5 

289.8 

281.4 

264.6 

248.0 

231.2 

214.4 

197.6 

180.8 

164.0 

88.5 

309.6 

300.6 

282.8 

265.0 

247.2 

229.4 

211.4 

193.6 

175.8 

94.0 

328.2 

318.8 

300.0 

281.2 

262.4 

243.6 

224.8 

206.0 

187.2 

99.5 

348.8 

338.8 

319.0 

299.4 

279.6 

269.8 

240.0 

220.2 

200.4 

105.5 

368.8 

358.4 

337.6 

316.8 

296.0 

275.2 

254.4 

233.6 

212.8 

111.5 

389.2 

378.2 

356.4 

334.6 

312.8 

291.0 

269.2 

247.4 

225.4 

117.5 

409.8 

398.2 

375.4 

352.G 

329.8 

306.8 

284.0 

261.2 

238.4 

123.5 

204 


STEEL  CONSTRUCTION 


1 

TABLE  VII  (Continued) 
Safe  Loads  on   Bethlehem  Columns 

t^,.             <*•  J 

k 

8*  H-Section 
Safe  loads  are  given  in  Thousands  of  Pounds 

U-,_| 

Section 
Number 

.Weicht 
Section 
Lb. 
per  Ft. 

Dimensions.  Inches 

Section 
8*.  In. 

Least 
Radius 
of  Gvr. 
Inches 

UNSUPPORTED  LENGTH 

D 

T 

B 

8 

9 

10 

11 

12 

31.5 

7H 

A 

8.00 

9.17 

1.98 

115.6 

111.8 

107.8 

104.0 

100.0 

34.5 

8 

H 

8.00 

10.17 

2.01 

12S.S 

124.4 

120.2 

116.0 

111.8 

39.0 

Vi 

T96 

S.04 

11.50 

2.03 

146.6 

141.2 

136.4 

131.6 

126.8 

43.5 

*K 

H 

8.08 

12.83 

2.04 

163.0 

157.8 

152.4 

147.2 

141.8 

48.0 

8N 

H 

8.12 

14.18 

2.05 

180.4 

174.6 

168.S 

163.0 

157.2 

53.0 

SM 

% 

8.16 

15.53 

2.07 

198.0 

191.8 

185.4 

179.2 

172.8 

57.5 

& 

H 

8.20 

16.90 

2.08 

215.8 

209.0 

202.2 

195.4 

188.4 

62.0 

8M 

K 

8.24 

18.27 

2.09 

233.6 

226.2 

218.8 

211.6 

204.2 

H8 

67.0 

8H 

H 

8.28 

19.66 

2.11 

252.0 

244.2 

236'.2 

228.4 

220.6 

71.5 

9 

i 

8.32 

21.05 

2.12 

270.0 

261.8 

253.4 

245.0 

236.8 

76.5 

OH 

I* 

8.36 

22.46 

2.13 

288.4 

279.6 

270.8 

262.0 

253.0 

81.0 

OK 

iK 

8.39 

23.78 

2.14 

305.8 

296.4 

287.2 

277.8 

268.4 

85.5 

OH 

ti 

8.43 

25.20 

2.16 

324.S 

315.0 

305.2 

295.4 

285.6 

90.5 

8.47 

26.64 

2.17 

343.8 

333.4 

323.2 

312.8 

302.4 

STEEL  CONSTRUCTION 


TABLE  VH  (Continued) 

Formula  P=  16,000-70^                                   '  j  r^fH 

in  which         P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches                                                          ^ 

1  =  length  in  inches                                                          Jl  

To  the  left  of  heavy  line  values  of  —do  not  exceed  12( 

>    L—  *-H 

OF  COLUMNS  IN  FEET 

Weight 

13 

14 

15 

16 

17 

18 

20 

22 

24 

Section 
Lb. 
per  Foot 

96.2 

92.2 

88.4 

84.4 

80.6 

76.6 

69.0 

61.0 

53.4 

31.5 

107.  -1 

103.2 

99.0 

94.8 

90.4 

86.2 

77.8 

69.2 

60.8 

34.5 

122.2 

117.4 

112.6 

107.8 

103.2 

98.4 

88.8 

79.4 

69.8 

39.0 

136.6 

131.4 

126.0 

120.8 

115.4 

110.2 

99.6 

89.0 

78.4 

43.5 

151.4 

145.6 

139.8 

134.0 

128.2 

122.2 

1106 

99.0 

87.4 

48.0 

166.6 

160.2 

154.0 

147.6 

141.4 

135.0 

122.4 

109.8 

97.2 

53.0 

181.6 

174.8 

168.0 

161.2 

154.4 

147.6 

133.8 

120.2 

106.6 

57.5 

196.8 

189.6 

182.2 

174.8 

167.4 

160.2 

145.4 

130.8 

116.0 

62.0 

212.8 

205.0 

197.2 

189.4 

181.6 

173.6 

158.0 

142.4 

126.8 

67.0 

228.-1 

220.0 

211.6 

203.4 

195.0 

186.6 

170.0 

153.4 

136.6 

71.5 

244.2 

235.4 

226.4 

217.6 

208.8 

200.0 

182.2 

164.4 

146.8 

76.5 

259.2 

249.8 

240.4 

231.2 

221.8 

212.4 

193.8 

175.2 

156.4 

81.0 

266.0 

256.2 

246.4 

236.6 

226.8 

207.2 

187.6 

168.0 

85.5 

292.2 

281.8 

271.6 

261.2 

251.0 

240.6 

220.0 

199.4 

178.8 

90.5 

206 


STEEL  CONSTRUCTION 


TABLE  VII  (Continued) 

Safe  Loads  on  Bethlehem  Columns 

Girder  Beams  Used  as  Columns 

Safe  loads  are  given  in  Thousands  of  Pounds 

Section 
Number 

Depth 
of  Beam 
Inches 

Weight 

per  Foot 
Pounds 

Area  of 
Section 
Sq.  In. 

Least 
Rad.  of 
Gyr.  In. 

UNSUPPORTED  LENGTH 

8 

9 

10 

11 

12 

G30a 

30 

200 

58.71 

3.28 

819.0 

804.0 

789.0 

774.0 

759.0 

G30 

30 

180 

53.00 

2.86 

723.4 

708.0 

692.4 

676.8  . 

661.2 

G28a 

28 

180 

52.86 

3.18 

734.0 

720.C 

7C6.2 

692.2 

678.2 

G28 

28 

165 

48.47 

2.77 

658.0 

643.2 

628.6 

613.8 

599.2 

G26a 

26 

160 

46.91 

3.05 

647.2 

634.2 

621.4 

608.4 

595.6 

G26 

26 

150 

43.94 

2.68 

592.8 

579.0 

565.4 

551.6 

537.8 

G24a 

24 

140 

41.16 

2.90 

563.2 

551.2 

539.4 

527.4 

515.4 

G24 

24 

120 

35.38 

2.66 

476.6 

465.6 

454.4 

443.2 

432.0 

G20a 

20 

140 

41.19 

2.91 

564.0 

552.0 

540.2 

528.2 

516.4 

G20 

20 

112 

32.81 

2.70 

443.2 

433.0 

422.8 

412.6 

402.4 

G18 

18 

92 

27.12 

2.59 

363.6 

354.8 

346.0 

337.2 

328.4 

G15b 

15 

140 

41.27 

2.83 

562.4 

550.0 

537.8 

525.6 

513.4 

G15a 

15 

104 

30.50 

2.64 

410.4 

400.6 

391.0 

381.2 

371.6 

G15 

15 

73 

21.49 

2.39 

283.4 

275.8 

268.4 

260.8 

253.2 

G12a 

12 

70 

20.58 

2.36 

270.6 

263.4 

256.0 

248.8 

241.4 

G12 

12 

55 

16.18 

2.24 

210.4 

204.2 

198.2 

192.2 

186.0 

G10 

10 

44 

12.95 

2.10 

165.8 

160.6 

155.4 

150.2 

145.0 

G9 

9 

38 

11.22 

1.98 

141.4 

136.6 

132.0 

127.2 

122.4 

G8 

8 

32.5 

9.54 

1.86 

118.2 

113.8 

109.6 

105.2 

101.0 

Beams  not  secured  against  yielding  sideways  and  free  to  fail  in  direction  of  least  radius 

of  gyration. 

STEEL  CONSTRUCTION 


207 


TABLE  VII  (Continued) 
Formula  P=  16,  000-70^- 

in  which    P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches 
I  =  length  in  inches. 

To  the  left  of  heavy  line  values  of  -  do  not  exceed  120 

OF  COLUMNS  IN  FEET 

Weight 
per  Ft. 
Pounds 

13 

14 

15 

16 

18 

20 

22     24 

28 

32 

36 

743.8 

6-15.6 

664.2 
5S4.4 

5S2.6 
524.0 

503.6 
420.8 

504.4 
392.2 

310.6 

501.0 
•3G1.S 
245.6 

234.0 
180.0 

139.8 
117.6 
06.6 

728.8 
630.0 

650.2 
569.8 

569.6 
G10.2 

491.6 
409.6 

492.6 
382.0 

310.8 

48S.8 
352.2 
238.0 

226.8 
174.0 

134.6 
112.8 
92.4 

713.8 
614.6 

636.4 
555.0 

556.8 
496.4 

479.8 
398.4 

480.6 
371.8 

302.0 

476.6 
342.4 
230.6 

219.4 
167.8 

129.4 
108.2 
88.0 

698.8 
599.0 

622.4 
540.4 

543.8 
482.6 

467.8 
387.4 

468.8 
361.6 

293.2 

464.4 
332.8 
223.0 

212.0 
161.8 

124.4 
103.4 
83.8 

668.8 
567.8 

594.4 
511.0 

518.0 
455.2 

444.0 
365.0 

445.0 
341.2 

275.6 

439.8 
313.4 
207.8 

197.4 
149.6 

114.0 
93.S 
75.0 

638.6 
536.6 

566.4 
481.6 

492.2 
427.6 

420.2 
342.6 

421.2 

320.8 

258.0 

415.4 
294.0 
192.8 

182.8 
137.6 

103.6 

608.6 
505.6 

538.6 
452.2 

466.4 
400.0 

396.2 
320.2 

397.4 
300.4 

240.4 

390.8 
274.4' 
177.6 

168.2 
125.4 

578.6 
474.4 

510.6 
422.8 

440.4 
372.6 

372.4 

518.4 
412.2 

454.8 
364.0 

388.8 

45S.2 

398.0 
287.6 

343.0 

200 
180 

180 
165 

160 
150 

140 
120 

140 
112 

92 

110 
104 
73 

70 
55 

44 
38 
32.5 

349.8 

399.0 
305.2 

337.2 
262.4 

277.0 
208.6 

278.6 
198.4 

152.4 

268.4 
177.4 

317.4 

324.8 

298.0 

373.6 
280.0 

222.8 

366.4 
255.0 

ir.2.o 

253.2 

326.2 

239.2 
187.6 

317.4 

216.2 
132.4 

124.2 

89.0 

153.4 
113.2 

82.8 

93.2 
74.8 
57.8 

84.4 
66.4 

208 


STEEL  CONSTRUCTION 


TABLE  VII  (Continued) 

Safe  Loads  on  Bethlehem  Columns 

I  -Beams  Used  as  Columns 

Safe  Loads  are  given  in  Thousands  of  Pounds 

Sertion 
Number 

Depth 
of  Beam 
Inchea 

Weight 
per  Foot 
Pounds 

Area  of 
Section 
Si.  In. 

Least 
Had.  of 
Gyr.  In. 

UNSUPPORTED  LENGTH 

5 

6 

7 

8 

9 

10 

B30 

30 

120 

35.30 

2.16 

496.2 

482.4 

4688 

455.0 

441.2 

427.6 

B28 

28 

105 

30.88 

2.06 

431.2 

418.6 

406.0 

393.4 

380.8 

368.2 

B26 

26 

90 

26.49 

1.95 

366.8 

355.4 

344.0 

332.6 

321.2 

309.8 

B24a 

24 

84 

24.80 

1.92 

342.6 

331.8 

320.8 

310.0 

299.2 

288.4 

24 

83 

24.59 

1.78 

335.4 

323.8 

312.2 

300.6 

289.0 

277.4 

B24 

24 

73 

21.47 

1.86 

295.0 

285.4 

275.6 

266.0 

256.2 

246.6 

B20a 

20 

82 

24.17 

1.82 

331.0 

319.8 

308.6 

297.4 

286.4 

275.2 

20 

72 

21.37 

1.88 

294.2 

284.6 

275.0 

265.6 

256.0 

246.4 

20 

69 

20.26 

1.59 

270.6 

260.0 

249.2 

238.6 

227.8 

217.2 

B20 

20 

64 

18.86 

1.62 

252.8 

243.0 

233.4 

223.6 

213.8 

204.0. 

20 

59 

17.36 

1.66 

233.8 

225.0 

216.2 

207.4 

198.6 

190.0 

18 

59 

17.40 

1.50 

229.6 

220.0 

210.2 

200.4 

190.8 

181.0 

B18 

18 

54 

15.87 

1.54 

210.6 

202.0 

193.4 

184.6 

176.0 

167.4 

18 

52 

15.24 

1.56 

202.8 

194.6 

186.4 

178.2 

170.0 

161.8 

18 

48,5 

14.25 

1.59 

190.4 

182.8 

175.4 

167.8 

160.2 

152.8 

B15b 

15 

71 

•20.95 

1.71 

283.8 

273.4 

263.2 

252.8 

242.6 

232.2 

B15a 

15 

64 

18.81 

1.49 

248.0 

237.4 

226.8 

216.2 

205.6 

195.0 

15 

54 

15.88 

1.55 

211.0 

202.4 

193.8 

185.2 

176.6 

168.0 

15 

46 

13.52 

1.36 

174.6 

166.2 

157.8 

149.6 

141.2 

132.8 

B15 

15 

41 

12.02 

1.41 

156.6 

149.4 

142.2 

135.0 

127.8 

120.8 

15 

38 

11.27 

1.44 

147.4 

140.8 

134.4 

127.8 

121.2 

114.6 

B12a 

12 

36 

10.61 

1.42 

138.4 

132.2 

125.8 

119.6 

113.2 

107.0 

12 

32 

9.44 

1.30 

120.6 

114.4 

108.4 

102.2 

96.2 

90.0 

B12 

12 

28.5 

8.42 

1.35 

108.6 

103.2 

98.0 

92.8 

87.6 

82.4 

BIO 

10 

28.5 

8.34 

1.21 

104.4 

98.8 

93.0 

87.2 

81.4 

75.6 

10 

23.5 

6.94 

1.27 

88.0 

83.4 

79.0 

74.4 

69.8 

65.2 

Beams  not  secured  against  yielding  sideways  and  free  to  fail  in  direction  of  least  radius 
of  gyration. 

STEEL  CONSTRUCTION 


209 


TABLE  VII  (Continued) 
Formula  P=  16,000-70^ 

in  which    P  =  unit  stress  in  pounds  per  square  inch 
r=  radius  of  gyration  in  inches 
1  =  length  in  inches 

To  the  left  of  heavy  line  values  of  —  do  not  exceed  120 

OF  COLUMNS  IN  FEET 

Weight 
per  Foot 
Pounds 

11 

12 

13 

14 

15 

16 

18 

20 

22 

24 

413.8 

400.0 

386.4 

372.6 

358.8 

345.2 

317.6 

290.2 

262.8 

235.4 

120 

355.6 
298.4 

343.0 
287.0 

330.4 
275.4 

317.8 
264.0 

305.2 
252.6  . 

292.6 
241.2 

267.4 
218.4 

242.2 

217.0 

172.8 

191.8 

105 

90 

195.6 

277.4 

266.6 

255.8 

245.0 

234.0 

223.2 

201.6 

179.8 

158.2 

84 

265.8 

254.2 

242.6 

231.0 

219.4 

207.8 

184.6 

161.4 

138.2 

83 

236.8 

227.2 

217.4 

207.8 

198.0 

188.4 

169.0 

149.6 

130.2 

73 

2(54.0 

252.8 

241.6 

230.6 

219.4 

208.2 

186.0 

163.6 

141.4 

82 

236.8 
206.4 

227.4 
195.8 

217.8 
185.0 

208.2 
174.4 

198.6 
163.6 

189.2 
153.0 

170.0 

151.0 
110.0 

131.8 

72 
69 

131.4 

194.2 

184.4 

174.6 

164.8 

155.0 

145.2 

125.8 

106.2 

64 

181.2 
171.2 

172.4 
161.4 

163.6 
151.8 

154.8 
142.0 

146.0 
132.2 

137.2 

119.6 
103.0 

102.0 

59 
59 

122.4 

158.6 

150.0 

141.4 

132.8 

124.0 

115.4 

98.2 

54 

153.6 

145.4 

137.2 

129.0 

120.8 

112.6 

96.2 

52 

145.2 
222.0 
184.4 

137.6 
211.8 
173.8 

1302 
201.4 
163.2 

122.6 
191.2 
152.4 

115.0 

180.8 
141.8 

107.6 

92.4 
150.0 
110.0 

48.5 
71 
64 

170.6 

131.2 

159.4 

124.4 
113.6 

150.8 

116.2 
106.4 

142.2 

107.8 
99.2 

133.6 

125.0 

116.4 

82.8 
77.8 

99.2 

54 

46 
41 

99.4 

91.0 
85.0 

92.0 

108.0 

101.4 

94.8 

88.2 

81.8 

75.2 

38 

100.8 
84.0 

94.4 

77.8 

88.2 
71.8 

81.8 

75.6 
59.6 

69.4 

36 
32 

65.6 

77.0 
69.8 

71.8 
64.0 

66.6 

61.4 
52.4 

56.2 

28.5 
28.5 

58.2 

60.6 

56.0 

51.4 

46.8 

23.5 

210 


STEEL  CONSTRUCTION 


TABLE  VIII 

Safe  Loads  on  Channel  Columns 
6*,  7",  8*,  9',  and  10'  Channels 

Safe  Loads  are  given  in  Thousands  of  Pounds 

H 

2Cs 

2  Pis. 

r 

Area 
2  Pis 

Area 
Total 

UNSUPPORTED  LENGTH 

8' 

9' 

10' 

11' 

12' 

13' 

6"-8# 

Latt. 

2  33 

4.76 

62 

61 

59 

57 

55 

54 

" 

8X* 

2.32 

4.00 

8.76 

115 

112 

108 

105   |    102 

99 

" 

5 

2.32 

5  00 

9.76 

128 

124 

121    |    117 

114 

110 

1 

7"-9f# 

Latt. 

2  72 

5  70 

77 

75 

74  |     72 

70 

68 

" 

9Xi 

2.67 

4.50 

10.20 

138 

134 

131 

128 

125 

122 

" 

A 

2.67 

5  63 

11.33 

153 

149 

145 

142 

138 

135 

8'-lU# 

Latt. 

3  11 

6.70 

93 

91 

89 

87 

85 

84 

" 

lOXi 

3  03 

5.00 

11  70 

161 

158 

155 

152 

148 

145 

* 

A 

3.02 

6  25 

12.95 

178 

175 

171 

168 

164 

160 

" 

1 

3.01 

7  50 

14.20 

196 

192 

188 

184 

180 

176 

8"-13!# 

Latt. 

2  98 

8.08 

111 

109 

106 

104 

102 

100 

" 

10XA 

2  97 

6.25 

14  33 

197 

193 

189 

185 

181 

177 

" 

1 

2.96 

7.50 

15.58 

214 

210 

205 

201 

196 

192 

9"-13i# 

Latt. 

3.49 

7.78 

109 

107 

106 

104 

102 

100 

" 

ux* 

3  40 

5  50 

13.28 

IS6 

183 

180 

176 

173 

170 

" 

5 

3.38 

6.88 

14  66 

205 

202 

198 

195  |    191 

187 

" 

t 

3.36 

8.25 

16  03 

224 

220 

216 

212   |   208 

204 

1 

9"-15# 

Latt. 

3  40 

8.82 

124 

121 

119 

117 

115 

113 

" 

nxl 

3.36 

5  50 

14.32 

200 

197 

193 

190 

186 

183 

" 

A 

3.34 

6.88 

15.70 

220 

216 

212 

208 

204 

200 

" 

j 

3.33 

8.25 

17  07 

239 

235 

230 

226 

221 

217 

10"-  15# 

Latt. 

3  87 

8.92 

127 

125 

123 

121 

120 

118 

" 

12XA 

3  74 

7  50 

16.42 

233 

230 

226 

222 

218 

215 

" 

1 

3  72 

9  00 

17.92 

254 

250 

246 

242 

238 

234 

" 

A 

3  70 

10  50 

19  42 

275 

271 

267 

262 

258 

253 

" 

I 

3.68 

12  00 

20.92 

296 

292 

287 

282 

277 

272 

10"-20# 

Latt. 

3  66 

11.76 

167 

164 

161 

159 

156 

153 

" 

12  X  A 

3.64 

10  50 

22.26 

315 

310 

305 

300 

295 

289 

" 

I 

3  63 

12  00 

23  76 

336 

331 

325 

320 

314 

309 

" 

A 

3.62 

13.50 

25.26 

357 

351 

346 

340 

334 

328 

5 

3.61 

15  00 

26.76 

378 

372 

366 

360 

354 

348 

8' 

9' 

10' 

1V 

12' 

13' 

STEEL  CONSTRUCTION 


211 


TABLE  VIII  (Continued) 

Formula   P  =  16,000  -70  •£ 

in  which  P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches 
I  =  length  in  inches 

To  left  of  heavy  line  values  of  —  do  not  exceed  125 
To  right  of  heavy  line  values  of  —  do  not  exceed  150 

OF  COLUMN  IN  FEET 

14' 

15' 

16' 

17' 

18' 

19' 

20'  |  21' 

22' 

23' 

24' 

26' 

28' 

30' 

52 

50 

49 

47 

45 

43 

41 

40 

38 

36 

35 

32 

28 

96 

93 

89 

86 

83 

80 

77 

74 

70 

67 

64 

58 

51 

107 

103 

100 

96 

93 

89 

86 

82 

78 

75 

71 

64 

57 

1 

67 

65 

63   61  |  60|  58 

56|  54 

53 

51 

49 

45 

42 

38 

118 

115 

112 

109 

106 

102 

99 

96 

93 

90 

86  1  80 

73 

67 

131 

128 

124 

121 

L117 

113 

110 

106 

103 

99 

96  1  89 

81 

74 

82 

80 

78 

76 

75 

73 

71 

69  1  67  1  66 

64|  60 

57 

53 

142 

139 

136 

132 

129 

126 

122 

119 

116 

113 

109 

103 

96 

90 

157 

153 

150 

146 

142 

139 

136 

132 

128 

124 

121 

113 

106 

99 

172 

168 

164 

160 

156 

152 

148 

144 

140 

136 

132 

124 

116 

108 

97 

95 

93 

91 

88 

86 

84 

81 

79 

77 

75 

70 

66 

61 

173 

169 

164 

160 

156 

152 

148 

144 

140 

136 

132 

124 

116 

108 

187 

183 

179 

174 

170 

165 

161 

156 

152 

148 

143 

134 

125 

117 

98 

96 

95 

93 

91 

89 

87 

85 

83 

81 

80 

76 

72 

68 

166 

163 

160 

157 

153 

150 

147 

144 

140 

137 

134 

127 

121 

114 

184 

180 

176 

173 

169 

165 

162 

158 

154 

151 

147 

140 

133 

125 

200 

196 

192 

188 

184 

180 

176 

172 

168 

164 

160 

152 

144 

136 

111 

108 

L106 

104 

102 

100 

98 

95 

93 

91 

89 

85 

80 

76 

179 

175 

172 

168 

165 

161 

158 

154 

150 

147 

143 

136 

129 

122 

196 

192 

188 

184 

180 

176 

172 

168 

164 

160 

156 

149 

141 

133 

213 

209 

204 

200 

196 

192 

187 

183 

178 

174 

170 

161 

153 

144 

116 

114 

112 

110 

108 

106 

104 

102 

100 

98 

96 

92 

88 

85 

211  |  207 

204 

200 

196 

193 

189 

185 

182 

178 

174 

167 

159 

152 

230 

226 

222 

218 

214 

210 

206 

202 

198 

194 

190 

182 

173 

165 

249 

244 

240 

236 

231 

227 

223 

218 

214 

209 

205 

196 

187 

178 

268 

263 

258 

254 

249 

244 

239 

235 

230 

225 

220 

211 

201 

191 

150 

148 

145 

142  |  140 

137 

134 

132|  129 

126 

123 

118 

113 

107 

284 

279 

274 

269 

264 

2591  253 

248 

243  |  238  [  233 

223 

212 

202 

303 

298   292 

287 

281)  276 

270 

265 

259)  254  |  248 

237 

226 

215 

322 

316   310 

305 

299)  293 

287 

281 

2751  269  |  263 

252 

240 

228 

341 

335   329 

322 

3161  3101  304 

297 

291  |  285 

279 

267  |  254 

241 

14' 

15'   16' 

17' 

18'  19'  20'  21'  22'  23' 

24' 

26'  28' 

30' 

212 


STEEL  CONSTRUCTION 


TABLE  VIII  (Continued) 

Safe  Loads  on  Channel  Columns 
12"  Channels 

Safe  Loads  are  given  in  Thousands  of  Pounds 

2  Us 

2  Pis. 

r 

Area 
2  Pis. 

Area 
Total 

UNSUPPORTED  LENGTH 

8' 

9' 

10' 

IV 

12' 

13' 

12*-20£# 

Latt. 

4.61 

12.06 

.175 

173 

171 

169 

167 

164 

" 

14XA 

4.40 

8.75 

20.81 

301 

297 

293 

289 

285 

281 

" 

i 

4  38 

10  50 

22  56 

326 

322 

317 

313 

309' 

304 

" 

A 

4.35 

12  25 

24.31 

352 

346 

342 

337 

333 

328 

" 

i 

4  33 

14  00 

26  06 

377 

371 

366 

361 

356 

351 

12"-25# 

Latt. 

4.43 

14;  70 

213 

210 

207 

204 

202 

199 

" 

14XA 

4.30 

12.25 

26.95 

389 

384 

378 

373 

368 

363 

" 

1 

4  29 

14.00 

28.70 

414 

409 

403 

397 

392 

386 

" 

5 

4.27 

15.75 

30.45 

439 

433 

427 

421 

415 

409 

" 

4  26 

17.50 

32.20 

464 

458 

452 

445 

439 

433 

" 

s 

4  25 

19.25 

33.95 

489 

483 

476 

469 

463 

456 

" 

i 

4.24 

21.00 

35.70 

514 

507 

500 

493 

486 

479 

12"-30# 

Latt. 

4.28 

17  64 

255 

251 

247 

244 

241 

237 

" 

14X& 

4.23 

15.75 

33.39 

481 

474  |  468 

461 

455 

448 

" 

! 

4.22 

17.50 

35.14 

506 

499 

492 

485 

478 

471 

" 

fi 

4.21 

19.25 

36.89 

531 

524 

517 

509 

502 

494 

" 

4.20 

21.00 

38  64 

556 

549 

541 

533 

525 

518 

" 

i 

4.20 

22.75 

40  39 

582 

574 

566 

557 

549 

541 

" 

4  19 

24.50 

42.14 

607 

598 

590 

581 

573 

564 

" 

-i 

4.18 

26.25 

43.89 

632 

623 

614 

605 

597 

588 

" 

i 

4  18 

28.00 

45.64 

657 

648 

639 

630 

620 

611 

12"-35# 

Latt. 

4  17 

20.58 

296 

292 

288 

284 

280 

276 

" 

14XH 

4  17 

19  25 

39.83 

573 

565 

557 

549 

541 

533 

" 

4  16 

21  00 

41.58 

598 

590 

581 

573 

565 

556 

" 

1 

4.16 

22.75 

43.33 

623 

614 

606 

597 

588 

579 

" 

4.15 

24.50 

45.08 

648 

639 

630 

621 

612 

603 

" 

H 

4.  .15 

26.25 

46.83 

674 

664 

655 

645 

635 

626 

" 

4.14 

28  00 

48.58 

699 

689 

679 

669 

659 

649 

" 

H 

4.14 

31  50 

52.08 

749 

738 

727 

717 

706 

696 

" 

H 

4.13 

35.00 

55  58 

799 

787 

776 

765 

753 

742 

8' 

9' 

10' 

11' 

12' 

13' 

STEEL  CONSTRUCTION 


213 


TABLE  VIII  (Continued) 

Formula   P=  16,000-70  -£• 

in  which   P  =  unit  stress  in  pounds  per  square  inch 
r  =  radius  of  gyration  in  inches 
1  =  length  in  inches 

To  left  of  heavy  line  values  of  —  do  not  exceed  125 
To  right  of  heavy  line  values  of  —  do  not  exceed  150 

n 

OF  COLUMN  IN  FEET 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 

162 

160 

158 

156 

153 

151 

149 

147 

145 

142 

140 

136 

131 

127 

277 

273 

269 

265 

261 

257 

253 

250 

246 

242 

238 

230 

222 

214 

300 

296 

291 

287 

283 

279 

274 

270 

266 

261 

257 

248 

240 

231 

323 

318 

314 

309 

304 

300 

295 

290 

286 

281 

276 

267 

257 

248 

346 

341 

336 

331 

326 

321 

316 

311 

306 

301  |  295 

285 

275 

265 

196 

193 

191 

188 

185 

182 

179 

177 

174 

171 

168 

183 

157 

152 

357 

352 

347 

342 

336 

331 

326 

321 

315 

310 

305 

294 

284 

273 

381 

375 

369 

364 

358 

352 

347 

341 

335 

330 

324 

313 

302 

291 

403 

397 

391 

385 

379 

373 

367 

361 

355 

349 

343 

331 

319 

308 

426 

420 

413 

407 

401 

394 

388 

382 

375 

369 

363 

350 

337 

325 

449 

442 

436 

429 

422 

416 

409 

402 

395 

389 

382 

369 

355 

342 

472 

465 

458 

451 

444 

437 

430 

423 

415 

408 

401 

387 

373 

359 

234 

230 

227 

223 

220 

216 

213 

210 

206 

203 

199 

192 

185 

178 

441 

435 

428 

421 

415 

408 

402 

395 

388 

382 

375 

362 

349 

335 

464 

457 

450 

443 

436 

429 

422 

415 

408 

401 

394 

380 

366 

352 

487 

480 

472 

465 

458 

450 

443 

436 

428 

421 

414 

399 

384 

370 

510 

502 

495 

487 

479 

471 

464 

456  |  448 

440 

433 

417 

402 

386 

533 

525 

517 

509 

501 

493 

485 

477 

469 

460 

452 

436 

420 

404 

556 

548 

539 

531 

522 

514 

505 

497 

488 

480 

472 

455 

438 

421 

579 

570 

561 

552 

543 

535 

526 

517 

508 

499 

491 

473 

455 

438 

602 

593 

583 

574 

565 

556 

547 

538 

529 

519 

510 

492 

473 

455 

271 

267 

263 

259 

255 

^250 

246 

242 

238 

234 

230 

221 

L213 

205 

525 

517 

509 

501 

493 

485 

477 

469 

461 

453 

445 

429 

413 

397 

548 

539 

531 

523 

514 

506 

497 

489 

480 

472 

464 

447 

430 

413 

571 

562 

553 

545 

536 

527 

518 

510 

501 

492 

483 

466 

448 

431 

594 

584 

575 

566 

557 

548 

539 

530 

520 

511 

502 

484 

466 

448 

617 

607 

597 

588 

579 

569 

559 

550 

541 

531 

522 

503 

484 

465 

639 

629 

619 

610 

600 

590 

580 

570 

560 

550 

541 

521 

501 

481 

685 

675 

664 

653 

643 

632 

622 

611 

601 

590!  580 

558 

537 

516 

731 

720 

708 

697 

686 

674 

663 

652 

640 

629 

618 

595 

572 

550 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 

214 


STEEL  CONSTRUCTION 


TABLE  VIII     (Continued) 

Safe  Loads  on  Channel  Columns 
12"  and  15"  Channels 

Safe  Loads  are  given  in  Thousands  of  Pounds 

II 

=r 
2» 

20 

2  Pis. 

r 

Area 
2  Pis. 

Area 
Total 

UNSUPPORTED  &ENGTH 

8' 

9' 

10' 

11' 

12' 

13' 

12*-40# 

Latt. 

4.09 

23.52 

338 

333 

328 

323 

318 

314 

" 

14  X'| 

4.12 

22.75 

46.27 

66-5 

655 

646 

636 

627 

618 

." 

4.11 

24.50 

48.02 

690 

680 

670 

660 

651 

641 

a 

1 

4.11 

26.25 

49.77 

715 

705 

695 

684 

674 

664 

" 

4.11 

28.00 

51.52 

740 

730 

719 

708 

698 

687 

" 

H 

4.10 

31.50 

55.02 

790 

779 

768 

757 

745 

734 

" 

u 

4.10 

35.00 

58.52 

840 

828 

816 

804  |  792 

780 

" 

if 

4.10 

,38.50 

62.02 

891 

878  j 

865 

853 

840 

8!?7 

4 

4.09 

42.00 

65.52 

941 

927 

914 

900 

887 

873 

15*-33# 

Latt. 

4.98 

19.80 

290 

287 

283 

280 

277 

273 

" 

16X    I 

4.84 

12.00 

31.80 

465 

459 

453 

448 

443 

437 

" 

A 

4.83 

14.00 

33.80 

494 

488 

482 

476 

470 

464 

" 

1 

4.82 

16.00 

35.80 

523 

517 

510 

504 

498 

492 

2 

* 

4.80 

20.00 

39.80 

581 

574 

567 

560 

553 

546 

a 

1 

4.79 

24.00 

43.80 

639 

632 

624 

616 

609 

601 

" 

4.76 

32.00 

51.80 

756 

747 

738 

728 

719 

710 

l5*-35# 

Latt. 

4.94 

20.58 

301 

298 

294 

291 

287 

284 

" 

16X    i' 

4.81 

16.00 

36.58 

534 

528 

521 

515 

508 

502 

" 

4.79 

20.00 

40.58 

592 

585  |  578 

571 

564 

557 

" 

4.77 

24.00 

44.58 

650 

642 

635 

627 

619 

611 

" 

1 

4.75 

32  00 

52  58 

767 

758 

748 

739 

730 

720 

11 

Q 

4.72 

48  00 

68.58 

1000 

988 

975 

963 

950 

938 

15MO# 

Latt. 

4.84 

23.52 

344 

340 

335 

331 

327 

323 

" 

16X   $ 

4.75 

16.00 

39  52 

576 

569 

562 

555 

548 

541 

" 

4  74 

20.00 

43.52 

635 

627 

619 

611 

604 

596 

" 

4.73 

24.00 

47  52 

693 

684 

676 

668  |  659 

651 

" 

1 

4.71 

32  00 

55.52 

809  . 

799 

789 

780  |  770 

760 

" 

o 

4.69 

48  00 

71.52 

1042 

1029 

1016 

1003 

991 

978 

41 

2 

4.68 

64.00 

87  52 

1274 

1259 

1243 

1227 

1211 

1196 

15'-45# 

16X    1 

4.H9 

20  00 

46.48 

677 

669 

660 

652 

644 

635 

" 

f 

4  68 

24.00 

50.48 

735 

726 

717 

708 

699 

690 

44 

1 

4  68 

32.00 

58.48 

851 

841 

830 

820 

809 

799 

44 

Q 

4  66 

48.00 

74.48 

1084 

1071 

1058  |1044 

1031 

1017 

44 

4  66 

64  00 

90.  48 

317 

1301 

1285 

1268 

1252 

1235 

15'~50# 

16X1 

4  64 

32  00 

61.42 

894 

883 

872 

861 

849 

838 

" 

Q 

4  64 

48.00 

77.42 

1126 

1112 

1098 

1084 

1070 

1056 

" 

2 

4.63 

64.00 

93  42 

1359 

1342 

1325 

1308 

1291 

1274 

g 

4  63 

SO.  00 

109  42 

592 

1572 

1552 

1532 

1312 

1492 

8' 

9' 

10' 

ir 

12' 

13' 

STEEL  CONSTRUCTION 


215 


TABLE 

Formula 

in  which  P  =  unit  s1 
r  =  radius 
/  =  length 

To  left  of  heavy  lin 
To  right  of  heavy  li] 

VIII  (Cor 

itinu 

K)0- 

nds  p< 
in  in 

-  do 
ido 

ed) 

70  l 

,ress  in  pou 
of  gyration 
in  inches 

e  values  of 
ae  values  of 

70  r 
?r  square  inch 
abet 

aot  exceed  125 
not  exceed  150 

P~~ 

OF  COLUMNS  IN  FEET 

14' 

15' 

16' 

17'  i  18'  19' 

20'  |  21'  |  22' 

23'  24' 

26' 

28'  30' 

i 

1    1 

309 

304   299 

294J  289 

285 

280|  275 

270 

265 

260|  251 

241  231 

608 

599  |  589 

580 

570 

561 

552 

542 

533 

523 

514 

495  |  476  |  457 

531 

621 

611 

602 

592 

582 

572 

562 

552 

543 

533 

513 

494 

474 

654 

644 

634 

624J  613)  603  |  593 

583  |  572  |  562  |  552 

532 

512 

491 

677 

666 

656 

646  |  635 

624  1  614|  6031_592J_582 

571 

551 

530 

509 

722 

711 

700   689 

677 

666|  655  |  644)  632 

621 

610  1  587Lj5S5 

542 

768  |  756 

744   732 

720  |  708 

696  684 

672 

660 

648 

624 

600 

576 

814 

802 

789 

776 

763 

751 

738LJ726 

713 

700 

687 

662 

636 

611 

860 

846 

833 

820 

806 

793 

779 

766 

752 

739 

725 

698 

672 

645 

270 

267 

263 

260  1  257 

253 

250 

247 

243  |  240 

237 

230 

223 

217 

432  |  426 

420 

415  |  409 

404  |  398 

393 

387 

382 

376 

365 

354 

343 

458 

^53 

447 

441 

435 

429 

423 

417 

411 

406 

400 

388 

376 

364 

485 

479 

473 

467 

460 

454 

448 

442 

435 

429 

423 

411 

398 

386 

539 

532 

525 

518 

511  |  504  j  497 

490 

483 

476 

470J  456 

442 

428 

593 

586 

578 

570 

562  |  555 

547 

540 

532 

524 

L516|  501 

486 

470 

701 

692 

683 

673 

664 

655 

646 

637 

628 

619 

609 

591 

573 

554 

280 

277 

273 

270 

266 

263 

259 

256 

252 

249 

245 

238 

231 

224 

496 

489 

483 

477 

470 

464 

458 

451 

445 

438 

432 

419 

406 

394 

549  |  542   535 

528 

521  |  514  T  507  |  500  |  493 

486 

478 

464  |  450|  436 

603 

596 

588 

580 

572  |  564  |  556 

548  |  541 

533 

525 

509 

494 

478 

711 

702 

693. 

683 

674  |  665  |  655 

646 

637 

627 

618 

599 

581 

562 

926 

914   902 

890 

878  |  866  |  853 

841 

828 

816 

804 

780 

756 

731 

319 

315   311 

307 

303  |  299 

295 

290 

286 

282)  278 

270 

262 

254 

534 

527 

520 

513 

506  |  499 

492 

485 

478 

47  1|  464 

450 

436 

422 

588 

581 

573 

565 

557 

550 

542 

534 

527 

519 

511 

496 

480|  465 

642 

634 

625 

617 

608 

600  |  592 

583 

575 

566 

558 

541 

524 

507 

750 

740 

730 

720  |  710 

700  |  690 

680  |  67  1|  661 

651  1  631 

611 

591 

965 

952 

939 

926 

914  1  901 

888  |  875  |  863  |  850 

837 

811 

785 

760 

1181 

1165 

1149 

1133 

1118 

1102 

1086 

1070 

1055 

1039 

1023 

992  |  960 

929 

627  |  619 

610 

602 

594 

586 

577 

569 

561 

552 

544 

527 

510 

494 

681  |  672 

663 

654 

645 

636 

626 

617 

608 

599 

590 

572 

554 

536 

789  !  778 

768 

757 

747 

736 

726 

715 

705 

694 

684 

663 

642 

620 

1003 

990 

976 

963 

950  |  936)  923)  909 

896 

883 

869  |  842 

816 

789 

1219 

1  202 

1186 

1170 

1  1  54 

1137  |11  21  11  105 

1088 

107211056 

1023 

991 

958 

827 

816 

805 

794 

783 

771  |  76QI  749 

738 

727  j  716 

6915 

671 

649 

1042 

1028 

1014 

1000 

986)  972|  95S|  944 

930 

916|  902 

874 

846 

818 

1257  [1241 

1224 

1206 

1189 

1172 

1156|1139 

1122 

1105(1087 

1054 

1020 

987 

1473  j  1453 

1433 

1413 

1393 

1373 

1354|1334|1314 

1294|1274 

123411195 

1156 

14'   15' 

16' 

17'  | 

18'  19' 

20'  21'  22'  23'  |  24' 

26'  |  28'  |  30' 

216 


STEEL  CONSTRUCTION 


Details  of  Construction.  Splices.  The  several  columns  in  a 
stack  may  be  made  in  one-,  two-,  or  three-story  lengths.  Two- 
story  lengths  are  most  commonly 
used.  The  one-story  length  per- 
mits each  story  of  the  column  to 
be  designed  for  the  load  in  that 
story,  whereas  a  two-story  col- 
umn is  designed  for  the  load  in 
the  lower  of  the  two  stories,  the 
same  section  being  used  through- 
out the  two-story  length;  this 
gives  a  greater  area  in  the  upper 
story  than  is  required  for  the 
stress  in  that  story.  Similarly, 
for  the  three-story  column  the 
middle  and  upper  stories  are  ex- 
cessive; also  the  three-story  col- 
rig.  145.  Splice  in  a  Channel  Column 

umn  is  more  difficult  to  erect. 

The  saving  in  favor  of  the  one-story  column  is  offset  by  the  expense 
of  the  splices  for  material,  shop  labor,  and  erection;  hence  the 
common  use  of  the  two-story  lengths. 

The  splice  is  placed  above  the  floor  line  a  sufficient  distance  so 

that  the  splice  plates  will  not  in- 
terfere with  the  beam  connec- 
tions; usually  18  inches  is  enough 
space.  The  strength  of  the  splice 
plates  may  vary  from  a  nominal 
amount  to  the  full  strength  of  the 
column,  generally  the  former,  it 
being  considered  that  the  splice 
plates  serve  only  to  hold  the  col- 
umns rigidly  in  line.  Even  when 
there  is  bending  stress  due  to 
eccentric  loads,  it  seldom  hap- 
pens that  there  is  actual  tension 
on  one  side  of  the  column,  hence 
the  splice  plates  do  not  transmit 

Fig.  146.     Splice  in  a  Plate  and  Angle  Column      any  StrCSS. 


STEEL  CONSTRUCTION  217 


As  the  splice  plates  are  not  designed  to  carry  stress,  the  load 
must  be  transmitted  by  direct  bearing  of  the  upper  column  on  the 
lower.  This  requires  that  the  ends  be  milled  exactly  at  right  angles 
to  the  axis  of  the  columns  and  that  the  end  of  the  upper  column 
have  full  bearing  on  the  top  of  the  lower  column,  or,  if  this  cannot 
be  had  on  account  of  change  in  size  or  shape  of  columns,  then  that 
a  bearing  plate  be  used  between  the  column  sections. 

Fig.  145  shows  a  column  splice  in  which  the  upper  section  of 
column  rests  directly  on  the  lower  section.  The  splice  is  made  by 
means  of  the  plates  m  and  the  angles  o.  The  plates  n  are  fillers 
which  make  up  the  difference  in  width  of  the  two  sections  of  column. 
The  angles  o  are  used  on  the  web  of  the  channels  because  plates 
could  not  be  riveted  on  after  the  columns  are  in  place. 

Fig.  146  shows  a  column  splice  in  which  the  upper  section  of 
column  does  not  rest  directly. on  the  lower  section.  In  addition  to 


Fig.  147.     Types  of  Lacing  for  Columns 

the  splice  plates  m,  there  are  required  the  filler  plates  n,  the  bearing 
plate  p,  and  the  'connection  angles  o. 

No  rules  can  be  given  for  the  thickness  of  splice  plates,  but  they 
should  be  made  consistent  with  the  column  section. 

Riveting.  The  specifications  for  riveting,  p.  365,  govern  the 
rivet  spacing  in  columns.  Refer  to  these  specifications  and  note 
the  spacing  at  the  ends  and  the  maximum  spacing.  It  is  interesting, 
as  an  indication  of  relative  cost,  to  note  the  number  of  lines  of  rivets 
required  for  various  styles  of  columns  as  follows: 

Plate  and  angle  columns  without  cover  plates 2  rows 

Plate  and  angle  columns  with  cover  plates .  .  4  or  6  rows 

Channel  columns 4  rows 

Bethlehem  columns  with  cover  plates 4  rows 

Zee-bar  columns  without  cover  plates 2  rows 

Zee* bar  columns  with  cover  plates G  rows 

Lacing.    Schneider's  Specifications*  contain  provisions  regard-' 

•"Specifications  for  Structural  Steel  for  Building",  by  C.  C.  Schneider,  M.  Am.  Soc.  C.  E., 
Transaction  American  Society  of  Civil  Engineers,  Vol.  LIV.  p.  449. 


218 


STEEL  CONSTRUCTION 


ing  lattice  bars,  p.  365.  Fig.  147  shows  the  style  of  lacing  referred 
to.  At  the  ends  of  laced  columns  tie  plates  are  required.  These 
plates  should  have  a  length  not  less  than  the  width  of  the  member. 
Tie  plates  must  also  be  used  where  beams  connect  to  the  column 
and  when  the  lacing  must  be  omitted  for  any  cause. 

Connections.  Connections  for  beams  and  girders  are  described 
and  illustrated  under  the  discussion  of  beams  and  girders.  The 
methods  there  given  will  enable  the  designer  to  work  out  any  special 
connections  required. 

Brackets.  Brackets  projecting  to  a  considerable  distance  from 
the  face  of  columns  are  used  for  supporting  cornices,  balconies,  etc. 
If  the  bracket  is  constructed  with  a  solid  web  plate  and  with  parallel 
flanges,  it  may  be  designed  as  a  cantilever  girder.  The  bracket  may 


Fig.  148.     Bracket  on  Column 

be  made  up  of  a  tie  and  a  strut,  Fig.  148,  with  no  web  plate.  In 
this  case  the  stresses  are  determined  by  the  methods  given  in  "Stat- 
ics". To  illustrate,  use  the  data  given  in  Fig.  148-a  and  the  stress 
diagram,  Fig.  148-b.  For  a  load  of  18,000  pounds  on  the  end  of  the 
bracket,  the  stress  in  the  tie  is  18,000  pounds  and  the  stress  in  the 
strut  is  25,200  pounds.  The  tie  and  strut  can  now  be  designed  by 
the  methods  given  for  tension  and  compression  members.  It  is  very 
important  to  keep  in  mind  that  loads  on  all  projecting  brackets  are 
eccentric  loads  on  the  columns  and  the  columns  must  be  designed 
accordingly 

Bases.    As  the  allowable  pressure  on  the  masonry  foundation 
of  the  column  is  very  much  less  than  the  stress  in  the  column,  it  is 


STEEL  CONSTRUCTION 


219 


necessary  to  provide  a  base  plate  to  spread  the  load  over  the  required 
area  of  the  masonry.  Whatever  the  form  of  base  used,  the  bottom 
of  the  column  section  must  be  milled  and  the  top  of  the  base  must 
be  also  a  flat  surface.  If  a  steel  plate  is  used,  it  will  be  true  enough 
without  milling,  but  all  other  forms  require  milling  to  give  a  true 
top  surface.  Two  or  more  angles  are  riveted  to  the  bottom  of  the 
column  to  provide  a  means  of  bolting  the  column  to  the  base,  Fig. 
149.  This  bolting  is  done  chiefly  for  assistance  in  erection. 


Fig.  149.     Details  of  Bottom  of  Column 

The  bases  are  usually  set  exactly  to  elevation  and  alignment 
before  the  columns  are  set.  This  makes  it  easy  to  get  the  columns 
in  their  correct  position.  The  bases  are  first  supported  on  wedges 
and  then  the  space  under  them  grouted. 

Flat  Plates.  The  simplest  form  of  column  base  is  a  flat  plate, 
which  may  be  either  steel  or  cast  iron.  Having  the  load  on  the 
column  and  the  allowable  unit  pressure  on  the  masonry,  the  area 


220 


STEEL  CONSTRUCTION 


of  the  plate  is  computed  therefrom.  The  thickness  of  the  plate  is 
computed  in  the  same  manner  as  bearing  plates  for  beams,  p.  130. 
The  thickest  steel  plate  ordinarily  available  is  1  inch  and  this 
limits  the  size  of  steel  plate  that  can  be  used.  However,  steel  slabs 
up  to  12  inches  thick  can  be  had  from  the  rolling  mills  if  the  quan- 
tity is  large  and  considerable  time  can  be  allowed  for  delivery.  They 
are  designed  in  the  same  manner  as  plates  of  ordinary  thickness 
except  that  the  unit  stress  from  bending  should  be  14,000  pounds 
per  square  inch.  There  is  not  likely  to  be  any  economy  in  using 
steel  slabs  when  there  is  room  for  using  cast-iron  pedestals. 

Cast-iron  plates  can  be  made  of  any  thickness,  but  when  the 
thickness  would  be  greater  than  4  inches,  it  becomes  economical  to 
use  cast-iron  pedestals.  Fig.  150  is  a  cast-iron  plate.  The  hole  in 
the  center  is  for  grouting.  In  this  form  of  plate  the  bolts  must  be 

in  place  before  the  plate  is  set ; 
the  bottom  of  the  plate  is 
recessed  for  the  bolt  heads. 

Cast- Iron  Pedestals.  When 
the  size  of  the  required  base 
is  so  great  that  a  flat  plate  is 
not  practicable,  the  cast-iron 
pedestal  is  used,  Fig.  151.  It 
is  impossible  to  compute  the 
stresses  in  a  cast-iron  pedestal 
with  any  certainty.  However, 

Fig.  isu.   Cast-iron  Base.  Plate  it  is  customary  to  design  them 

by  the  flexure  formula,  which 

seems  to  give  results  that  are  satisfactory.  This  cannot  be  done 
directly,  hence  the  dimensions  must  be  assumed  or  determined  from 
other  considerations,  and  the  resulting  section  checked  by  computing 
its  resisting  moment. 

Illustrative  Example.  Assume  that  the  load  on  a  column  is 
600,000  pounds  and  the  unit  bearing  on  masonry  is  500  pounds  per 
square  inch.  Then  the  area  required  is 

600,000     10An 

•      *       =1200  sq.  m. 

Use  a  plate  3'-0"X3'-0",  which  gives  an  area  slightly  in  excess 
of  the  amount  required. 


RECESS  rox 

BOLT  HEAD 


B-O  TO  3-0  J 


J-0  TO  S'OSQUAfie BASE..  S.o  To  6'.o'  SQUA*£  BASE. 

Fig.  151.    Types  of  Cast-Iron  Pedestals 


222 


STEEL  CONSTRUCTION 


The  size  of  the  top  plate  is  determined  by  the  size  of  the  column 
and  its  connection  angles.     In  this  case  assume  20  inches. 

The  height  must  be  assumed.    It  may  vary  between  one-third  and 

one-half  the  base.     Use  16  inches. 
•  The  diameter  of  the  hub  is 
assumed.     Use  8  inches  inside. 

The  thickness  of  metal  must 
be  assumed  for  trial.  Use  1  J-inch 
for  hub;  1J  inches  for  top  plate; 
and  If  inches  for  base  plate. 

The  shaded  area  in  Fig.  152 

Fig.  152.    Be^f^Cggpj^Stoe.ttkol     sh()ws   the    ^^    available   for 

resisting  bending.    To  determine 

its  resisting  moment  R  M  it  is  first  necessary  to  locate  its  neutral 
axis  and  then  compute  its  moment  of  inertia. 

The  center  of  gravity  is  found  by  the  method  given  on  p.  36. 
The  area  of  the  cross  section  is 

fora  area  =  33" X  If"  =  57.75 
for  b  area=  2"X13"XH"  =  32.50 
ford  area=  2"x6"Xli"  =  15.00 

105. 25  sq.  in. 
Taking  moments  about  the  bottom  line 

fora  moment  =  57. 75  X  .875=  50.53 
for  6  moment  =  32.50X  8.25  =268.12 
ford  moment  =  15. 00X15. 375  =  230. 62 

549.27 

The  distance  from  the  bottom  of  the  plate  to  the  neutral  axis  0-0  is 
c  _549.27_r      „ 

105.25    ' 

The  moment  of  inertia  about  the  axis  0-0  is 
/from  tables 
=  \57.75X(4.33) 

/from  tables 
=  \32.50X  (3. 04) 

ffrom  tables 


fora        1  = 


for  b        7  = 


ford 


15 

1083 

458 
301 

2 

\15X(10.16)3  1548 

3407 


STEEL  CONSTRUCTION  223 

The  allowable  stress  on  cast  iron  in  tension  is  3000  pounds  per 
square  inch.    Then  the  resisting  moment  of  the  section  is 

30°OX3407 


5.21 


=  1  ,940,000  in.-lb. 


The  bending  moment  M,  resulting  from  the  pressure  on  the 
bottom  of  the  plate,  is  determined  by  treating  the  plate  as  an 
inverted  cantilever,  Fig.  152. 

Then  M  =  300,  000X9  =  2,  700,000  in.-lb. 

This  amount  is  excessive  because  it  assumes  the  column  load  applied 
at  a  point  at  the  center  of  the  top  of  the  plate,  whereas  it  occupies 
considerable  area. 

As  the  bending  moment  computed  for  the  load  is  2,700,000 
inch-pounds  and  the  resisting  moment  is  1,940,000  inch-pounds,  the 
trial  section  is  not  sufficient.  The  section  can  be  increased  in 
strength  by  increasing  the  height  or  by  increasing  the  thickness  of 
metal.  The  most  effective  places  for  additional  metal  are  -in  the 
top  and  bottom  plates. 

PROBLEM 

Increase  the  height  of  the  cast-iron  pedestal  to  T-G",  retaining  all  other 
dimensions.  Compute  the  resisting  moment. 

Number  of  Ribs.  The  number  of  ribs  to  be  used  can  be  as 
indicated  by  the  bases  shown  in  Fig.  151.  Therefore,  12  ribs  are 
used  for  the  case  illustrated  above.  The  thickness  of  the  rib 
should  be  not  less  than  1  inch  and  about  TV  the  clear  height  be- 
tween the  bottom  and  top  plates.  Also  there  must  be  enough 
section  in  the  ribs  and  hub  just  below  the  top  plate  to  take  the  whole 
load  at  10,000  pounds  per  square  inch.  In  this  case  the  clear  height 
is  13  inches,  which  indicates  1-inch  ribs.  This  thickness  gives 
ample  section  for  compression. 

Shape  of  Pedestal.  Cast-iron  pedestals  may  be  made  round 
instead  of  square  if  so  desired,  Fig.  151.  The  round  pedestal  has 
some  advantages  in  manufacture  and  is  especially  well  suited  for 
round  piers.  The  bending  moment  on  a  round  base  is  approxi- 
mately the  total  column  load  multiplied  by  0.10  of  the  diameter  of 
the  plate.  The  resisting  moment  of  the  pedestal  is  computed  by 
the  method  given  above* 


224 


STEEL  CONSTRUCTION 


When  a  rim  is  used  around  the  edge  of  the  bottom  plate,  it  can 
be  computed  in  the  section  resisting  bending.  This  rim  is  desirable 
in  large  pedestals. 

There  must  always  be  a  grout  hole  at  or  near  the  center  of  the 
pedestal.  In  large  plates  additional  holes  are  used. 

Steel  Grillage.  If  the  masonry  bearing  is  long  and  narrow,  steel 
I-beams  may  be  used  for  spreading  the  load.  When  so  used,  they 
are  designed  in  the  same  manner  as  given  for  bearings  for  beams, 
p.  133.  These  beams  rest  directly  on  the  masonry,  and  are  filled 


£_BOTH  FL'ffS  FOR  GROUT 

3•IS-^4  'xiopx  S-O.  L  ONG 
-i.s -JXJXj 'x I '-I /'ABOUT 
\GPIND   TO  FIT 
/O-PLTS.-6"xJ'xi 
ZO-BOLTS$  * XI- 6-? HEX  NUTS 
/-PLT  ZtXlkl:4    {BOL  T) 


Fig.  153.     Steel  Grillage  Designed  for  Base  of  a  Column  ol  a  16  Story  Building 

with  cement,  concrete,  or  grout.  The  webs  of  the  beams  must  be 
investigated  for  shearing  strength  and,  if  at  all  deficient,  tight- 
fitting  separators  must  be  used.  Separators  should  be  used  in  any 
case  to  hold  the  beams  in  position. 

The  flanges  of  I-beams  are  not  always  exactly  at  right  angles 
to  the  webs,  hence  the  beams  may  not  furnish  a  flat  surface  for 
seating  the  columns.  This  makes  it  necessary  to  plane  enough  off 
the  top  of  beams  to  provide  a  true  surface  for  the  bottom  of  the 
column  to  rest  upon.  In  order  to  be  effective,  this  must  be  done 
after  the  beams  are  assembled  and  rigidly  held  together. 


STEEL  CONSTRUCTION  225 

The  load  from  the  column  must  be  properly  distributed  to  the 
beams  forming  the  grillage,  using  a  steel  or  cast-iron  plate  of  proper 
thickness.  It  may  be  necessary  in  some  cases  to  use  a  cast-iron 
pedestal  on  the  steel  grillage.  Fig.  153  shows  a  steel  grillage  designed 
for  the  base  of  a  column  of  a  16-story  building. 

CAST-IRON  COLUMNS 

Cast-iron  columns  formerly  were  used  extensively  for  building 
work,  even  for  fireproof  buildings  ten  or  more  stories  in  height. 
Now  they  are  used  only  for  small  buildings  of  non-fireproof  con- 
struction. The  change  has  come  about  through  greater  demand  for 
safety  and  the  reduction  in  cost  of  steel  columns. 

Characteristics.  Advantages.  The  advantages  of  cast-iron  col- 
umns are:  They  offer  greater  resistance  to  fire  than  unprotected 
steel  columns.  They  generally  can  be  more  quickly  obtained. 
They  can  be  made  of  any  desired  shape  and  ornamented  to  suit 
the  requirements  of  architectural  design.  They  occupy  a  minimum 
of  space  in  the  building. 

Disadvantages.  Cast-iron  columns  have  the  following  disad- 
vantages: For  supporting  a  given  load  a  cast-iron  column  costs  more 
than  a  steel  column.  They  are  subject  to  defects  that  are  difficult 
to  discover  by  usual  methods  of  inspection. 

Cast-iron  columns  are  made  to  order.  As  the  brackets  and 
flanges  must  be  cast  on  the  column  shaft  at  the  time  it  is  made,  it 
is  not  possible  to  have  the  column  shafts  in  stock. 

Cast  iron  is  subject  to  considerable  variation  in  quality,  depend- 
ing upon  the  materials  used  in  the  melt  and  the  treatment  in  the 
furnace  and  in  the  molds.  It  may  be  soft  and  tough,  or  hard  and 
brittle.  It  is  made  in  'small  foundries,  as  compared  with  the  rolling 
mills  which  make  structural  steel.  Hence  it  is  not  possible  to 
control  the  quality  closely,  as  can  be  done  with  steel. 

Blow  holes  in  castings  are  spaces  which  the  iron  does  not  fill, 
due  to  bubbles  of  air  or  gas  becoming  entrapped  in  the  mold.  Sand 
pockets  may  be  formed  by  the  dropping  of  sand  from  the  molds. 
In  both  of  these  cases  the  surface  of  the  casting  may  be  perfect,  and 
the  defects  thus  difficult  or  impossible fto  find. 

The  most  frequent  fault  with  round  columns  is  eccentricity, 
due  to  displacement  of  the  core.  The  core  may  sag  in  the  mold,  due 


226 


STEEL  CONSTRUCTION 


Fig.  154.     An  Eccentric 
Cast-Iron  Column 


to  its  weight,  or  it  may  float  in  the  liquid  iron.  The  result  is  shown 
in  Fig.  154.  It  may  occur  at  any  place  in  the  length  of  the  column. 
At  the  ends  the  fault  is  easily  detected,  but  at 
intermediate  points  it  is  necessary  to  drill  test 
holes  as  indicated  in  the  figure.  The  test  holes 
should  be  drilled  in  the  top  or  in  the  bottom  of 
the  casting  in  reference  to  its  position  in  the 
mold.  An  eccentricity. of  §  inch  causes  appre- 
ciable loss  of  strength.  A  greater  amount  than 
this  should  cause  rejection. 

Column  Sections.  Unless  there  is  some  rea- 
son for  using  a  special  shape,  cast-iron  columns  are  made  round.  The 
size  is  designated  by  the  external  diameter  and  the  thickness  of  metal. 
The  sizes  commonly  made  for  structural  purposes  vary  from  6  inches 
to  15  inches  in  diameter  and  from  J  inch  to  2|  inches  in  thickness. 
Special  sections  sometimes  used  are  shown  in  Fig.  155.  The 
angles,  U-shapes,  and  square  sections  are  used  chiefly  for  store  front 
work.  They  are  generally  made  with  the  exposed  surfaces  paneled 
or  otherwise  ornamented. 

H-shaped  columns  may  be  used  for  general  purposes.  They  are 
not  as  economical  as  round  columns,  hence  are  not  much  used.  In 
some  respects  they  are  better  than  round  columns  as  connections 


Fig.   155.     Typical  Cast-Iron  Column  Sections 


are  easily  made  and  all  surfaces  are  open  to  inspection,  making  it 
easier  to  find  defects. 

Method  of  Design.  The  method  of  designing  cast-iron  columns 
is  similar  to  that  used  in  designing  steel  columns.  The  direct  load 
and  the  concentric  equivalent  of  eccentric  loads,  if  any,  are  com- 
puted in  the  same  manner.  The  allowable  unit  stress  is  computed 
from  a  formula  similar  to  that  for  steel  columns.  The  formula 
given  under  Unit  Stresses,  p.^  51,  is 

P  =10,000 -GO  - 
r 


STEEL  CONSTRUCTION 


227 


Eccentric   Loading.    The   concentric   equivalent   for  eccentric 
loads  is  computed  by  the  same  formula  as  used  for  steel  columns, 


For  round  cast-iron  columns  an  approximate  formula  is 


in  which  M  is  the  eccentric  moment  in  inch-pounds  and  d  is  the 
diameter  of  the  column  in  inches. 

Fig.  156  shows  two  cases  of  eccentric  loading  of  a  round  column. 
For  the  load  m,  the  eccentricity  em  is  the  distance  from  the  center  of 
the  column  to  the  center  of  the  web  of  the  beam.  For  the  load  n, 


Fig.  156.     Diagrams  Showing  Eccentric  Loading  on  a  Round  Column 

the  eccentricity  en  is  the  distance  from  the  center  of  the  column  to  the 
center  of  bearing  on  the  bracket,  this  center  of  bearing  being  taken  at 
2  inches  from  the  face  of  the  column,  when  standard  brackets  are  used. 

On  page  177,  it  was  pointed  out  that  when  two  eccentric  loads 
act  about  the  axis  1-1  and  2-2,  respectively,  their  results  must  be 
added  together.  This  is  true  also  of  rectangular  and  round  cast- 
iron  columns.  But  for  round  columns  the  maximum  effect  of  two 
such  loads  is  somewhat  less  than  the  sum  of  their  separate  effects. 
The  resultant  varies  with  the  relative  amounts  of  the  eccentric 
moments,  but  the  difference  is  not  great  and  the  sum  of  the  separate 
effects  can  be  used  without  much  error. 

Factors  Required.  If  the  concentric  equivalent  load  is  used, 
the  only  properties  of  the  section  required  are:  area  A;  radius  of 


228  STEEL  CONSTRUCTION 

gyration  r;  and  distance  to  extreme  fiber  c.  The  values  of  these  prop- 
erties can  be  computed  for  the  rectangular  sections  by  the  methods 
given.  For  round  columns  the  area  is  computed  from  the  formula 


the  radius  of  gyration  is  computed  from  the  formula 


the  distance  c  is  \  d.  In  these  formulas  TT  is  3.1416;  d  is  outside 
diameter  of  column;  and  dv  is  inside  diameter  of  column.  The 
inside  diameter  equals  the  outside  diameter  less  twice  the  thickness 
of  metal.  Thus  a  column  8  inches  in  diameter  and  1  J  inches  thick- 
ness of  metal  has  an  inside  diameter  of  5  inches. 

llluslrative    Example.    Assume  a  column  with  the  following 
dimensions  and  loads,  and  determine  the  thickness  of  metal  required: 
Length  of  column  140" 

Concentric  load  from  column  above  1  60,000  # 
Eccentric  load  40,000  #-  eccentricity  7"   ' 
Outside  diameter  of  column  (assumed)  10* 

Then  the  eccentric  moment  is  40,000X7  =  280,000  in.-lb.  which  by 
the  rule  on  p.  175,  is  reduced  to  f  X  280,000  =  21  0,000  in.-lb. 
The  concentric  equivalent  is 


.  _ 

a  10 

The  total  load  for  which  the  column  must  be  designed  is 
Load  from  upper  column  160,000  # 

Eccentric  load  40,000 

Concentric  equivalent  load         105,000 

305,000  # 

It  is  now  necessary  to  assume  a  trial  thickness  of  metal  and  compute 
the  strength.    Assume  2  inches. 


A  =     (d2-d*)  =  X  (100-36)  =50.26  sq.  in. 


/  140 

P  =  10,000-60 -  =  10,000T60X^  =  7100#  per  sq.  in. 

T  2 .  y 

Total  capacity  7 1 00 X 50. 26  =  356,800 # 


TABLE  IX 

SAFE  LOADS  FOR  ROUND  CAST-IRON  COLUMNS 
Thousand  Pound  Units 

P=10,000-60  — 
Values  to  right  of  heavy  line  are  beyond  limit  of  length,  70  r. 


11- 

I' 

LENGTH 
FEET 

Weight  Ibs.  per) 
ft.  of  length 

** 

il" 

I 

Radius  of  „  | 
Gyration  » 

6 

8 

10 

12 

14 

16 

18 

20 

22 

6 

1 

81.7 

73.7  1   65.7 

57.8 

!        1 

33.2 

10.6 

38.6 

1.91 

j 

95.1)  85.6]  76.1 

66.6 

38.6)    12.4)     43.5 

1.87 

A 

107.8}  96.8)  85.8 

74.7) 

1 

44.0)    14.1]     47.6 

1.84 

1 

119.4(106.8)  94.3 

81.7 

1 

49.0)   15.7)     51.0 

1.80 

LI 

130.2]  11  6.2)  102.2 

8S.2 

53.8]   17.2)     53.9)1.77 

n 

140.2)124.8 

109.4 

93.9 

58.2)   18.6|     56.2 

1.74 

7 

118.7)109.2 

99.7|  90.2 

80.7 

46.0  1   14.7]     72.9|2.23 

135.2)124.1)113.0 

102.0 

90.91 

52.6|   16.8|     80.6|2.19 

i 

150.6 

138.0)125.4 

112.7 

100.1                                I 

58.9 

18.8)     87.212.15 

3 

165.1 

151.0)136.8)122.6 

108.4! 

64.8 

20.8|     92.9 

2.11 

Li 

178.9 

163.3J147.6  132.OJ116.4j 

70.7)  22.6)    97.7 

2.08 

ljs 

191.8 

174.7)157.6 

140.6J  123.5 

76.1)  24.3)   101.8 

2.05 

Ej 

203.8 

185.3)  166.8 

148.3  1129.8) 

81.1  1   25.9|    105.3  [2.02 

8 

142.2 

132.7  1123.2 

113.61104.0 

94.6) 

53.3!    17.1 

113.4 

2.58 

1 

162.6!  151.41  140.3)  129.2)  118.1 

107.0, 

61.3J   19.6 

126.2 

2.54 

181.9]  169.2  |156.6J  143.9]  131.2 

118.6 

68.6 

22.0 

137.4)2.50 

li. 

200.3]  186.1  1171.9,157.7)  143.4 

129.2; 

76.1)  24.3 

147.4 

2.46 

218.0  202.3 

186.6|170.9 

1  55.2  1  139.5 

82.7 

26.5 

156.1 

2.43 

i  ^ 

234.4j  217.2 

199.9  182.7J  165.3 

148.2) 

89.3)  28.6 

163.8 

2.39 

1 

250.3  231.6 

212.9 

194.2|175.5 

156.8 

94.8)  30.6 

170.4 

2.36 

9 

1  156.3 

146.6 

137.11127.5 

118.0 

108.4! 

60.6 

19.4 

166.8 

2.93 

j 

1  178.8 

167.7 

156.6]  145.4)  134.3 

123.2) 

69.8 

22.3     186.4 

2.89 

i 

200,5 

187.8 

175.1  1162.4  1149.7 

137.0 

78.41   25.1 

204.2 

2.85 

i  j 

221.3 

207.0 

192.8 

178.51164.2 

150.0) 

87.0)  27.8 

220.2  1  2.81 

i* 

241.3)225.5 

209.8  1194.0]  178.2 

162.5) 

94.91  30.4 

234.5J  2.78 

q 

260.1)242.8 

225.6)208.3 

1191.0 

173.7) 

103.0 

32.9    247.312.74 

n 

278.0 

259.2 

240.3)221.5 

202.6 

183.8 

110.3)  35.31  258.4 

2.70 

10 

1 

179.7)170.1 

160.5)151.0 

141.4 

131.8 

122.3 

68,2)  21.8)  234.6 

3.28 

1 

[231.81219.1)206.41193.7 

181.0)168.2 

155.5 

88.2 

28.3)   289.913.20 

n 

280.4 

264.6|248.8|233.0 

216.3|201.3 

185.5 

107.21   34.4|   335.6!  3.  13 

n 

324.9 

306.0)  287.1]  268.2 

249.3  1230.4 

211.5) 

125.0|  40.0)  373.lj3.05 

)365.9 

344.0)322.1)300.2 

278.3 

256.41234.4 

141.7)   45.4)   403.212.98 

11 

i 

263.2 

250.4  1237.7)  225.0  1212.2 

199,5  1186.7 

174.0 

98.0)   31.4)  396.7;  3.55 

ii 

319.4|303.6|287.7)271.8 

255.9)239.9)224.0 

208.1 

119.5 

38.3)   462.613.48 

IG 

371.8)352.9)  333.9)  315.0|  296.0)  277.0 

258.1  1  239.1 

139.7|  44.8!  517.8)3.40 

jj 

420.6)398.6!  376.6|  354.6!  332.6)  310.fi 

288.7  1  266.7 

158.7)   50.9]   563.5)3.33 

2 

465.6  1  440.6J415.6  j  390.6  1  365.6  1  340.7 

315.71290.7 

176.4)   56.5    601.0)3.26 

12 

1 

294.7(281.9]  269.2|  256,5)  243.81  231.0 

218.3!  204.7 

107.5)   34.6)   527.1|3.91 

n 

358.7  )  342.8  1  326.9  J  31  1  .OJ  295.2  1  279.3 

263.4  1  247.6 

131.4)   42.2)   618.213.83 

Q 

418.8)399.8)380.8)  361.8)  342.8)  323.8 

304.8 

285.8 

154.1 

49.5 

696.0)3.75 

1  J 

475.3]  453.3  1  43  1  .2  1  409.2  1  387.  1  1  365.  1 

343.0 

3  I'd.1 

175.5 

56,4 

761.8 

3.68 

2 

528.  1|  503.0  1478.0 

452.9  1427.8!  402.8 

377.7 

352.fi 

195.8 

62.8|  817.0)3.61 

13 

1 

326.0  1  3  1  3.3  1  300.5  1  287.8  1  275.0  1  262.3 

24<Ui  23'i.N 

117,5 

37.7 

683.5)4.26 

Li 

397.8  1381.  9)  366.0  [350.2  1  334.2  1  3  18.4  1  302.5  1  286.6 

143.9 

46.1 

805.3 

4.18 

465.8  1  446.8  1  427.7  1  408.7  1  389.7  1  370.6  1  351  .6  1  332.6 

169.0)   54.2|  911.3)4.10 

y 

529.8  1507.7|  485,5  1463.4  1441.2 

419.  1'  397.0  37  1> 

192.9)   61.911002.4)4.02 

2 

590.4  !  565.2  1  540.0  1  51  4.8  1  489.6  1  464.4  1  439.2  1  4  1  4.0 

215.6)   69.1)1080.2)3.95 

a 

Make  allowance  for  eccentricity  in  accordance  with  the  following  formu  a:  We'=5  -r 
FF'e'=Equivalent  concentric  load,  Ib.;  Af=Moment   of  eccentricity,  in.-lb.;and  d=Dia 
in.     See  pp.  227,  228. 

meter. 

230 


STEEL  CONSTRUCTION 


This  amount  is  greater  than  required,  so  the  thickness  may  be  reduced. 
It  can  be  shown  that  the  thickness  required  is  1  f  inches. 

PROBLEM 

From  the  data  given  above,  determine  the  thickness  required  for  a  column 
12  inches  in  diameter.  Note  that  eccentricity  is  8  inches  for  this  diameter 

Tables.  The  published  tables  of  strength  of  cast-iron  columns 
vary  greatly,  due  to  the  variety  of  formulas  used.  Columns  other 
than  round  are  used  so  little  and  when  used  are  so  likely  to  be  of 
special  dimensions  that  tables  of  strength  would  be  of  little  value. 
Table  IX  gives  the  strength  of  round  columns  in  accordance  with 
the  formula  adopted.  It  also  gives  the  value  of  r  for  use  in  comput- 
ing the  concentric  equivalent  for  eccentric  loads.  The  Chicago 
Building  Ordinance  from  which  this  formula  is  taken  limits  the 


Fig    157.     Splice  of  Cast-  Fig.  158.     Splices  of  Cast-Iron  Columns  by  Dowel  Plates 

Iron  Column  by  Flanges 

length  of  cast-iron  columns  to  70  Xr.    This  limit  is  marked  by  the 
heavy  zigzag  line  in  the  table. 

Illustrative  Example.    Determine  the  column  required  to  sup- 
port a  load  of  191,000  pounds,  the  length  being  11  feet. 
From  Table  IX  either  of  the  following  sizes  may  be  used: 

S"diam.  X If  metal 

9"diam.  XlJ"  metal 

10"diam.  Xl  "metal 

The  9-inch  column  is  the  lightest  and  will  be  used  if  no  special  con- 
sideration indicates  the  use  of  one  of  the  other  sizes. 


STEEL  CONSTRUCTION 


231 


PROBLEM 

The  loads  and  lengths  of  a  stack  of  cast-iron  columns  are  given  below. 
Dct  ermine  the  sections. 

4th  story,  column  load,  20,000#  length  13  ft.. 

3rd      "           "           "  70,000$  length  12  ft 

2nd     "      .     "     '••'     "  115,000#  length  14ft. 

1st       "           "     ,     "  155,000#  length  16  ft 

Basement       "           "  205,000$  length    9ft 


IO"&  9" 


All  seats   to  slope  £ 

All  Webs   on  lugs  to  be  f  thick. 

The  above  connections  have  capacities  corrtspondiny  to 
those  of  standard  connect/on  angles. 

The  distance  from  top  of  column  to  beam  seat  must 
be  sufficient  to  allow  a  clearance  of  £' Between  top  of  beam 
and   underside     of  flange    Or  bolt  head. 

Distance  A  will  vary  to  fit  position  of  holes  when 
beams    are  adapted  to  multiple  punch.   Otherwist  tht 
distance    A   will  be    for 
24"  Beams  «/.'    l5"Beoms  J/".    B'Becmy  jj.  6"Beoms  3" 

£>(?"    „      4",  if-    „     3j~  a"    »     4~. 

Id"       ,.        4-     10"  ^  „       3f.    7"    *        J/ 

Holes   should  btj    larger  than    corresponding  rivet 
holes   in  beam- 


8"  7"  &  6" 


Fig.  159.     American  Bridge  Company  Standard  Beam  Connections 


232 


STEEL  CONSTRUCTION 


Details  of  Construction.  Splices.  Splices  in  cast-iron  columns 
are  made  by  means  of  flanges  as  shown  in  Fig.  157.  The  load  is 
transmitted  from  upper  to  lower  column  by  bearing.  The  bearing 
surfaces  must  be  milled  exactly  at  right  angles  to  the  axis  of  the 
column.  If  the  sections  do  not  match,  the  metal  must  be  thickened 
as  shown  at  m  and  n  to  provide  the  bearing.  Some  manufacturers 
set  the  flanges  back  from  the  ends  of  the  column  to  reduce  the  area 


Fig.  160.     Double  Beam  Connections  to  Cast-Iron  Column; 


of  the  milled  surface.  The  flange  is  made  wide  enough  to  take  a 
row  of  1-inch  bolts.  Four  or  more  bolts  are  used. 

The  splice  can  be  made  by  means  of  a  dowel  plate.  It  is  not  so 
satisfactory  as  the  flange  splice.  It  is  used  when  there  is  no  space  avail- 
able for  the  flanges,  and  also  for  replacing  broken  flanges,  Fig.  158. 

Beam  Connections.  Beam  connections  are  made  by  mean's  of 
brackets  and  lugs  cast  on  the  column.  The  standard  connections 
designed  a*id  used  by  the  American  Bridge  Company  are  given  in 
Fig.  159.  The  entire  load  is  supported  by  the  bracket.  The  seat 


STEEL  CONSTRUCTION 


233 


of  the  bracket  slopes  so  that  the  beam  will  not  bear  on  the  end 
of  the  bracket  when  it  deflects.  The  lug  serves  to  tie  the  construc- 
tion together  and  to  hold  the  beam 
upright.  Bolts  must  be  use"d  for  all 
connections  to  cast  iron,  as  the  casting 
would  be  broken  by  driving  rivets. 

When  double  beams  are  used,  the 
connection  is  modified  as  shown  in  Fig. 
160.  This  figure  also  shows  brackets 
for  supporting  wood  beams.  Fig.  161 


Fig.  162.     Base  Plate  for  Cast-Iron  Columns 


Fig.  101.     Top  of  Cast-iron  Col- 
umn for  Supporting  I-Beams 

shows  the  detail  of  the  top  of  a  cast-iron  column  which  supports 
two  steel  beams. 

Bases.  Cast-iron  base  plates  or  cast-iron  pedestals  are  used 
for  cast-iron  columns.  They  are  designed  in  the  manner  described 
for  the  bases  of  steel  columns.  If  the  plate  is  used,  a  raised  cross 
is  cast  on  the  top  to  fit  inside  the  column  and  hold  it  in  place,  Fig. 
162.  If  the  pedestal  is  used,  the  top  of  it  is  made  to  match  the 
flange  cast  on  the  column. 

TENSION  MEMBERS 

Definition  and  Theory.  In  building  construction,  it  does  not 
often  occur  that  loads  must  be  supported  by  tension  members. 
Occasional  special  features,  such  as  balconies  or  stair  landings, 
require  this  form  of  support.  The  most  frequent  use  of  it  occurs 
in  trusses  (which  are  not  covered  in  this  work). 

Axial  Tension.  A  member  is  subjected  to  axial  tension  when 
the  load  is  applied  in  line  with  the  axis  of  the  member  in  a  way  that 
tends  to  stretch  or  pull  the  member  apart,  Fig.  163. 


234 


STEEL  CONSTRUCTION 


The  strength  of  steel  in  axial  tension  varies  directly  in  proportion 

to  the  net  cross-section  area,  not  being  affected  by  the  length  (except 

as  to  the  weight  of  the  member)  or  by  the  shape  of  the  section. 

Under  Unit  Stresses,  the  allowable  value  of  P  for  axial  tension  is 

given  as  16,000  pounds  per  square  inch;  then  the  strength 

]    of  a  section  is 


The  area  used  in  this  formula  must  be  the  net  area,  i.  e., 
the  smallest  area  at  any  section  in  the  length  of  the 
member. 

In  axial  tension  the  stress  is  assumed  to  be  distrib- 
uted over  the  entire  area,  as  indicated  in  Fig.  163.  This 
differs  from  the  tension  due  to  bending,  which  is  not 
uniformly  distributed  but  increases  from  nothing  at  the 
neutral  axis  to  a  maximum  at  the  extreme  fiber,  as  ex- 
plained on  p.  78. 

Tension  Due  to  Eccentricity.  As  in  the  case  of  com- 
Fif».  ins.  Dia-  pression  members,  the  load  on  a  tension  member  may  be 
fnTaTr^on  eccentric,  and  thus  produce  both  axial  tension  and  ten- 
sion due  to  bending.  The  discussion  of  concentric  and 
eccentric  loads  in  compression  applies  to  tension  members.  Fig.  164 
illustrates  the  stresses  from  an  eccentric  load  in  tension 
which  corresponds  to  Fig.  140  in  compression;  abed 
represents  the  total  axial  tension  and  a  b  the  axial  ten- 
sion per  square  inch  due  to  the  load  W;  bb'  represents 
the  tension  on  the  extreme  fiber  due  to  the  bending 
moment  We.  Then  the  total  extreme  fiber  stress  due 
to  the  load  IF'  is  a  bf.  The  concentric  equivalent  of 
an  eccentric  load,  as  for  compression,  is  expressed  by 
the  formula 


If  the  member  is  not  symmetrical,  the  value  of  c  to  be  Fig  164  Ditgram 
used  is  from  the  neutral  axis  to  the  extreme  fiber  on  the  fUS£*£S3i 
side  toward  the  eccentric  load. 

Eccentricity  in  tension  members  usually  results  from  the  form 
of  the  connection,  and  in  most  cases  it  can  be  avoided  by  careful 


STEEL  CONSTRUCTION 


235 


attention  to  the  details.  It  generally  will  be  more  economical  thus 
to  avoid  the  eccentricity  than  to  provide  the  additional  section 
necessary  to  resist  it.  In  altogether  too  many  cases  this  is  neglected. 
The  importance  of  the  effect  of  eccentricity  is  illustrated  by  the 
following  computations. 

Assume  a  load  of  100,000  pounds  concentric,  then  the  net  area 

required  is  —       —  or  6 . 25  square  inch.    Now  assume  the  same  load 
10,000 

with  an  eccentricity  of  1  inch,  a  value  of  c  equal  to  2|  inches  and  /» 
equal  to  1.9  inches.  The  concentric  equivalent  is 

"p&gfc*'* 

The  total  load  is  100,000+70,000  or  170,000  pounds,  and  the  area 

170  000 
required  is  l    —  or  10.6  square  inches.     In  this  case  it  requires 

lUjUUU 


ft)  .  (c) 

Fig.  105.     Types  of  Connections  for  Angles 


an  increase  of  70  per  cent  in  the  section  to  provide  for  the  eccentricity. 

Fig.  165-a  shows  a  single  angle  connected  by  one  leg.  It  is 
eccentric  about  both  axes.  Fig,  165-b  shows  a  pair  of  angles  each 
connected  by  one  leg.  This  is  eccentric  about  the  axis  1-1.  Fig. 
105-c  shows  two  views  of  the  same  pair  of  angles  m,  with  a  pair  of 
connection  angles  n  added,  which  eliminates  the  eccentricity. 

Sections.  Almost  any  form  of  steel  can  be  used  as  a  tension 
member.  The  choice  of  the  section  is  governed  largely  by  the 
connections  that  are  to  be  made  to  it.  Of  the  structural  shapes, 
angles,  plates,  and  channels  are  best  adapted  for  tension  members 
in  ordinary  building  work. 

Round  rods  are  used  for  tie-rods,  balcony  hangers,  temporary 
bracing,  and  other  similar  purposes. 


236 


STEEL  CONSTRUCTION 


Eyebars  are  seldom  used  in  building  work,  being  more  especially 
adapted  to  bridge  trusses.  They  may  be  used  where  heavy  loads 
occur  and  rigidity  is  not  important. 


Fig.  166.     Types  of  Connections  for  Hangers 


Net  Area.    Plates  and  shapes  in  tension  must  be  connected  by 
rivets  and  the  rivet  holes  must  be  deducted  to  determine  the  net 


vSTEEL  CONSTRUCTION  237 

area  of  cross  section.  The  number  of  rivet  holes  to  be  deducted  in 
any  case  depends  upon  their  arrangement  as  explained  on  p.  69. 
The  size  of  the  hole  deducted  is  J  inch  greater  than  the  nominal 
diameter  of  the  rivet.  This  allowance  is  an  arbitrary  one  to  cover 
the  actual  size  of  the  hole,  which  is  about  ^  inch  larger  than  the 
rivet,  and  to  compensate  for  injury  to  the  metal  around  the  hole 
due  to  punching.  Care  must  be  taken  to  arrange  the  rivet  holes 
so  as  to  retain  the  greatest  possible  area  at  the  critical  section. 

Round  rods  can  be  figured  full  size  if  the  ends  are  upset,  other- 
wise the  net  area  must  be  taken  at  the  root  of  the  thread.  When 
upset  ends  are  used,  they  are  made  large  enough  so  that  there  is  an 
excess  of  strength  in  the  threads,  making  the  whole  section  of  the 
rod  available.  Generally  the  threads  on  rods  are  cut,  but  they  can 
be  made  by  cold  rolling.  The  latter  method  makes  the  diameter  at 
the  root  of  the  thread  somewhat  less  than  the  diameter  of  the  body 
of  the  rod,  but  the  treatment  seems  to  make  the  steel  stronger. 
Tests  show  that  the  rolled  thread  is  stronger  than  the  rod  on  which 
it  is  rolled,  thus  making  the  whole  section  of  the  rod  available. 

Eyebar  heads  are  always  made  of  sufficient  size  to  develop  the 
strength  of  the  bar,  so  that  the  whole  section  is  available. 

Details  of  Connections.  Riveted  Connections.  Riveted  con- 
nections are  required  wrhen  structural  shapes  or  plates  are  used. 
Angles,  plates,  and  channels  are  most  commonly  used.  The  top 
connection  usually  is  made  with  a  gusset  plate  depending  from  a 
beam  or  girder.  Fig.  166  illustrates  a  number  of  such  connections. 
The  gusset  plate  may  be  spliced  into  the  web  of  a  plate  girder;  set 
in  between  two  channels;  may  be  an  extension  of  the  gusset  at  the 
joint  of  a  truss;  or  may  be  connected  by  angles  riveted  to  the  flange 
of  an  I-beam.  (See  p.  64).  The  requirements  for  the  top  connec- 
tion are  that  the  gusset  plate  shall  be  of  sufficient  thickness  to  give 
the  required  bearing  for  the  rivets;  and  that  the  rivets  connecting 
the  plate  to  the  beam  or  girder,  also  those  connecting  the  hanger 
to  the  gusset,  be  sufficient  in  number  and  be  placed  symmetrically 
about  the  axis  of  the  tensile  stress. 

It  has  been  noted  that  angles  in  tension  must  be  connected  by 
both  legs  to  avoid  eccentricity.  This  sort  of  connection  is  desirable 
for  the  further  purpose  of  distributing  the  stress  over  the  entire 
section  of  the  hanger  as  evenly  as  possible.  Angles  in  pairs  are 


238 


STEEL  CONSTRUCTION 


much  preferred  to  single  angles.    They  shduld  be  stitched  together 
with  rivets  and  ring  fillers  spaced  about  2  feet  apart. 


Fig.  107.     Turnbucklc  and  Sleeve  Nut 


The  connections  at  the  bottom  of  the  hanger  may  be  made 
with  gusset  plates  in  the  same  manner  as  at  the  top,  or  the  connect- 
ing members  may  be  attached  direct  to  the  hanger. 


rrh 


Fig.  1G8.     Types  of  End  Connections  for  Rods 

When  it  is  necessary  to  splice  a  tension  member,  it  is  evident 
that  the  splice  must  transmit  the  entire  stress  in  the  member.    The 

principles  involved  and  methods 
to  be  used  are  fully  explained 
under  Strength  of  Riveted  Joints, 
p.  67,  and  have  been  used  in 
designing  the  splices  in  plate 
girders. 

Details  of  Rods.  Rods  are 
specinlly  suited  for  adjustable 
members.  With  certain  forms  of 

Fig.  169.     Det  ails  of  End  Connection  of  Eyebar     Connections,   the   adjustment   Can 


STEEL  CONSTRUCTION  239 

be  made  at  the  ends;  with  splices,  the  adjustment  can  be  made  at 
the  splice.  A  rod  is  spliced  by  means  of  a  turnbuckle,  or  sleeve  nut, 
Fig.  1G7.  The  ends  are  threaded  right  and  left  to  make  the  member 
adjustable.  The  threaded  ends  are  upset  to  maintain  the  full 
strength  of  the  section.  The  various  forms  of  end  connections  are 
shown  in  Fig.  168.  They  need  no  explanation. 

Details  of  Eyebars.  Eyebars  must  be  connected  at  the  ends 
with  pins,  Fig.  169.  Refer  to  "Structural  Drafting"  for  details  of 
eyebars. 

WIND  BRACING 
GENERAL  CONDITIONS 

Horizontal  Pressures.  In  the  preceding  discussion,  the  loads 
considered  have  been  gravity  loads,  i.  e.,  loads  acting  vertically. 
In  addition  to  these  gravity  loads,  all  structures  are  subjected  to 
wind  loads,  or  pressures,  which  are  assumed  to  act  horizontally. 
Probably  no  locality  is  entirely  free  from  wind  storms,  so  it  is  always 
necessary  to  provide  for  wind  pressures  in  designing  the  framework 
of  buildings. 

It  is  assumed  that  wind  pressure  acts  horizontally  and  bears 
uniformly  over  the  entire  windward  surface  of  the  building,  and  that 
it  may  occur  in  any  direction.  These  assumptions  are  not  strictly 
correct.  The  wind  may  be  inclined,  due  to  the  contour  of  the 
ground  or  to  obstructions.  It  is  known  that  the  pressure  near  the 
top  of  a  building  is  greater  than  near  the  ground;  that  the  pressure 
is  not  uniform  over  large  areas;  that  the  rush  of  air  around  the 
corners  produces  greater  pressure  near  the  corners;  and  that  there 
is  a  suction  on  the  leeward  side  as  well  as  a  pressure  on  the  windward 
side.  The  wind  may  strike  the  building  at  any  angle,  but  the  maxi- 
mum effect  is  produced  when  it  strikes  squarely  against  the  side 
(or  end)  of  the  building.  While  the  above  variations  are  known  to 
be  true,  it  is  impossible  to  provide  for  them  in  detail,  hence  the 
assumption  stated  above  is  followed  and  leads  to  satisfactory 
results. 

Unit  Pressure.  Many  experiments  have  been  made  to  estab- 
lish the  relation  between  wind  velocity  and  wind  pressure.  While 
a  large  amount  of  data  has  been  developed,  the  mathematical 


240  STEEL  CONSTRUCTION 

relations  are  not  fully  established.  Furthermore,  it  is  not  certain 
what  maximum  velocity  should  be  provided  for.  Hence  it  is  the 
general  practice  to  use  an  assumed  pressure  in  pounds  per  square 
foot  of  the  surface.  The  amount  assumed  varies.  In  some  cities 
the  building  ordinances  specify  the  amount  to  be  used ;  some  specify 
20  pounds  per  square  foot;  others,  30  pounds.  The  writer  recom- 
mends that  the  framework  of  all  buildings  be  designed  to  resist  a 
wind  pressure  of  20  pounds  per  square  foot  on  the  surface  of  the 
building.  It  can  reasonably  be  assumed  that  the  partitions  and 
walls  will  add  enough  to  the  strength  so  that  the  completed  struc- 
ture will  resist  a  pressure  of  30  pounds  per  square  foot.  Walls 
should  not  be  counted  as  resisting  any  part  of  the  20  pounds,  unless 
practically  solid,  i.  e.,  without  openings.  The  above  recommenda- 
tions should  be  followed  with  some  discretion :  increasing  the  amount 
carried  by  the  framework  in  very  high  buildings,  and  in  buildings 
which  have  few  partitions  or  a  very  large  percentage  of  openings  in 
the  walls;  decreasing  the  amount  in  low  buildings,  and  in  buildings 
which  have  masonry  cross  walls.  In  buildings  having  outside 
bearing  walls  of  masonry  and  a  reasonable  amount  of  cross  walls, 
or  partitions,  these  parts  may  be  relied  upon  to  resist  the  entire 
wind  pressure,  provided  the  height  of  the  building  is  not  more  than 
twice  its  width. 

The  maximum  wind  pressure  occurs  only  at  long  intervals. 
It  is,  therefore,  allowable  to  use  higher  unit  stresses  for  wind  stresses 
than  for  gravity  stresses.  Under  Unit  Stresses  it  is  provided  that 
for  stresses  produced  by  wind  forces  alone,  or  combined  with  those 
from  live  and  dead  loads,  the  units  may  be  increased  fifty  per  cent 
over  those  given  for  live  load  and  dead  load  stresses ;  but  the  section 
shall  not  be  less  than  required,  if  wind  forces  be  neglected.  Gen- 
erally, the  members  required  to  support  the  gravity  loads  are  utilized 
for  the  wind  loads.  In  such  cases  no  additional  area  is  required  on 
account  of  the  wind  stress  unless  this  stress  exceeds  fifty  per  cent 
of  the  gravity  load  stress. 

Paths  of  Stress.  Transmission  of  Load  to  Foundation.  The 
total  wind  pressure  on  the  building  in  the  direction  under  considera- 
tion is  the  assumed  unit  pressure  per  square  foot  multiplied  by  the 
projected  area  exposed  to  the  pressure.  This  pressure  must  ulti- 
mately be  resisted  by  the  foundations  of  the  building.  Hence, 


STEEL  CONSTRUCTION 


241 


there  must  be  paths  for  transmitting  the  pressure  to  the  founda- 
tions from  the  area  to  which  it  is  applied.  The  pressure  is  applied 
directly  to  the  masonry  walls  and  windows  These  are  strong 
enough  as  ordinarily  built  to  carry  the  load  to  the  floors.  The  floor 
construction,  whether  of  tile  arches,  concrete,  or  even  wood  con- 
struction, acting  as  a  horizontal  girder,  transmits  the  load  to  the 
points  selected  for  applying  it  to  the  steel  framework.  Thence  the 
steel  framework  carries  the  load  to  the  foundation 

Routing  the  Stress.     The  de-    ,  ^_  .,_  , 

signer  has  some  choice  as  to  the 
steel  members  which  he  will  utilize 
for  carrying  the  wind  load  So 
far  as  the  steel  is  concerned  the 
shortest  path  is  the  best,  but  other 
considerations  may  require  the 
use  of  less  direct  courses,  most 
commonly  through  the  spandrel 
beams  around  the  outside  of  the 
building  Thus  in  Fig  170  is 
shown  a  plan  of  the  columns  of  a 
building,  with  the  typical  floor 
framing  The  heavier  lines  repre- 
sent girders  and  the  lighter  lines,  /7' 
joists. 

Considering  first  the  wind 
from  either  the  East  or  the  West, 
the  direction  of  the  load  is  par- 
allel to  the  narrow  way  of  the 
building  and  in  the  same  direc- 
tion as  the  floor  girders.  This  ^ 
situation  indicates  that  the  wind 
load  should  be  carried  down 
along  each  E.-W  row  of  columns,  viz,  1-4,  5-8,  9-12,  etc.  Then  each 
line  of  columns  and  its  girders  will  have  to  support  the  wind  pressure 
on  one  panel  of  the  face  of  the  building  from  top  to  bottom.  It  is 
probable  that  these  columns  and  girders  as  designed  for  the  gravity 
stresses  will  carry  the  wind  stresses.  (This  of  course  is  governed 
by  the  height  of  the  building.)  Now  if  it  were  decided  to  carry  the 


Fig.    170.    Framing  Plan  of  Building  for  Study 
of  Bracing  System 


242  STEEL  CONSTRUCTION 

entire  load  to  the  two  ends  and  carry  it  through  the  columns  and 
girders  L-4  and  25-28,  the  intensity  of  the  stresses  would  be  three 
times  as  great  and  probably  would  require  extra  metal  in  these 
members.  Therefore,  so  far  as  economy  of  steel  is  concerned, 
the  wind  load  should  be  carried  down  each  row  of  columns. 
But  it  may  happen  that,  in  order  to  do  this,  deep  brackets  are 
required  in  the  lower  stories  for  connecting  girders  to  columns, 
brackets  of  greater  size  than  is  permitted  by  the  architectural 
requirements;  then  it  becomes  necessary  to  carry  the  load  to  the 
ends,  where  the  spandrel  beams  and  their  connections  can  be 
made  as  large  as  need  be  A  combination  of  the  two  arrangements 
may  be  made,  the  load  above  a  certain  floor  being  carried  down 
on  each  row  of  columns,  and  that  below  being  carried  down  the 
end  rows. 

Next  considering  the  wind  from  the  North  or  the  South,  its 
direction  is  parallel  to  the  joists.  It  is  probable  that  these  joists 
are  not  strong  enough  to  take  the  wind  stresses  without  adding 
metal  to  that  required  for  the  gravity  stresses.  The  wind  pressure 
can  easily  be  carried  to  the  two  sides  of  the  building  along  the  lines 
1-25  and  4-28,  where  the  necessary  strength  in  the  spandrel  girders 
can  readily  be  obtained. 

The  foregoing  illustration  is  comparatively  simple;  most  cases 
are  not  so  easy  to  settle.  In  general  terms,  the  designer  should  take 
all  possible  advantage  of  interior  framing,  carrying  through  the 
spandrels  only  that  portion  of  the  wind  load  which  cannot  be  taken 
by  the  interior  framing. 

The  bracing  strength  of  the  interior  framing  is  limited  by  the 
strength  of  the  connections  to  the  columns  and  riot  by  the  strength 
of  the  girder  and  joist  sections.  The  maximum  bending  moments 
occur  at  these  connections,  and  to  develop  the  full  strength  of  the 
beams  would  require  larger  brackets  than  the  architectural  treat- 
ment would  permit.  So  generally  it  will  be  that  a  large  proportion 
of  the  wind  load  must  go  through  the  spandrel  beams  where  the 
limitations  as  to  depth  of  beams  and  size  of  brackets  are  not  so 
restricted. 

It  is  sometimes  possible  to  use  diagonal  members  for  bracing. 
They  make  the  most  direct  and  efficient  form  of  bracing,  and  should 
be  used  when  the  conditions  permit. 


STEEL  CONSTRUCTION 
SYSTEMS  OF  FRAMEWORK 


243 


A  horizontal  load  can  be  transmitted  vertically  by  means  of 
framework  by  two  systems:  (1)  by  triangular  framework,  Fig.  171, 


Fig.  171.     Diagram  of  Triangular  Framing.         Fig.  172.     Diagram  of  Rectangular  Framing 

having  axial  stresses;  and  (2)  by  rectangular  framework,  Fig.  172, 
having  bending  stresses.  ^ 

Triangular  Framework.  Single  Panels.  Fi£  173  shows  a 
single  panel  of  triangular  framing  supporting  the  horizontal  force  IF. 
The  reactions  at  the  foundations  are  R,  V,  and  V. 


Fig.  173.     Diagram  of  Stresses  in  Triangular 
Framing 


7=F'  =  — 
L 

By  inspection   it  is  to  be  seen 

that  the  stress  in  a  equals  W;  in 

c  equals  V.     The  stresses  in  b 

and  c  can  be  determined   from 

that  in  a  by  resolution  of  forces 

(See      Concurrent     Forces     in- 

"Statics"),  as  indicated  in  the  figure.     These  stresses  are  all  axial; 

a  and  c  in  compression ;  b  in  tension. 

When  the  values  of  //,  L,  and  W  are  known,  the  numerical 
values  for  a,  6,  c,  and  V  can  be  determined. 

Two  or  More  Horizontal  Panels.  Two  or  more  adjacent  panels 
can  be  used,  as  shown  in  Fig.  174.  It  is  first  necessary  to  divide 
the  load  between  the  two  panels.  It  is  simplest  to  divide  the  load 
equally,  irrespective  of  whether  the  panels  are  equal  in  length. 


244 


STEEL  CONSTRUCTION 


On  this. basis  the  stress  in  a  equals  W,  and  in  d  equals  \W.     By 
resolution,  the  stresses  in  6  and  c,  and  in  e  and/  can  be  determined. 
FA    equals  the   stress  in   c,    F3 
equals  the  stress  in/,  and  F2  is 
the  difference  in  stresses  c  and  /. 
If  in  this  case  Ll  equals  L2,  then 
the  stress  in  b  equals  stress  in  e\ 
the  stress  in  c  equals  the  stress 


in  /;    Fj 
equals  0. 


equals    F3;    and    F2       /., 


Fig.  174.     Diagram  of  Two  Horizontal  Panels 
of  Triangular  Framing 


PROBLEM 

Assume  four  panels  similar  to  those 
shown  in  Fig.  174.  Let  //  equal  16  feet; 
L,,  L2,  L3,  and  L4  equal  20  feet;  and  W 
equal  36,000  pounds.  Compute  the  stresses 
in  the  diagonals. 

Two  or  More  Vertical  Plincls. 
Two  or  more  panels  may  be  placed 
one  above  the  other  as  in  Fig.  175. 
In  this  case  R,  =  W,  +  TF8+JK2. 
The  value  of  Vl  =  F2  is  determined 
by  taking  moments  about  0  from 
which 


1 


Tig.  175.     Diagram  of  Vertical  Panels  of 
Triangular  Framing 


TF4(771+ff2+773) 
L 

The  stresses  in  the  members  a  to 
k  inclusive  can  be  determined  by 
the  methods  given  in  "Statics", 
when  the  values  of  IF4,  TFS,  JF2, 
H3,  7/2,  7/j,  and  L  are  known  and 
of  7?,  and  F,  are  computed. 


STEEL  CONSTRUCTION 


245 


PROBLEM 

In  Fig.  175  assume  W4  equals  10,000  pounds;  W3  equals  10,000  pounds; 
H' ,  equals  12,000  pounds;  //,  equals  18  feet;  7/2  equals  13  feet;  H3  equals  13  feet; 
L  equals  16  feet.  Determine  the  stresses  in  a  to  k  inclusive. 

Extension  of  Triangular  Framework.  Similarly,  the  triangular 
framework  can  be  extended  indefinitely  in  both  directions,  as  in 
Fig.  176.  For  convenience  in  solving  this  case  the  figure  can  be 
separated  into  horizontal  tiers,  or  stories,  and  each  computed.  In 
doing  this,  the  anti-reactions  of  one  tier  must  be  applied  as  loads 


/  \ 


/v- 


Fig.  17G.     Diagram  of  Triangular  Framing  Extending  Over  a  Building 

in  the  next  lower  tier.  The  horizontal  load  to  be  resisted  at  any 
tier  is  the  sum  of  all  the  horizontal  loads  above  that  tier; 
thus  the  horizontal  load  or  shear  at  the  top  of  the  first  story  is 


PROBLEM 

Assume  loads  and  dimensions  for  Fig.  176  and  compute  the  stresses  in 
the  diagonal  members. 


246 


STEEL  CONSTRUCTION 


In  Figs.  173  to  176  inclusive  the  diagonals  are  shown  in  one 
direction  only.     As  the  wind  may  come  from  either  direction,  both 


A    A 


r\ 


Fig.  177.     Diagram  of  Rectangular  Frame 
with  Hinged  Joints 


Fig.  178.     Diagram  of  Rectangular 
Frame  with  Rigid  Joints 


diagonals  will  be  used  in  all  cases.    In  certain  panels,  circumstan- 
ces may  prevent  the  use  of  any  diagonal  bracing,  Fig.  176,  in 


Fig.  179.     Diagram  of  Rectangular  Frame  Showing  Points  of  Contraflexure 

which  case  the  stresses  must  be  distributed  among  the  other  panels. 

Rectangular   Framework.    Single   Panel.    A   single   panel   of 

rectangular  framing  is  illustrated  in  Fig.  177.    The  four  corners 


STEEL  CONSTRUCTION  247 

are  represented  as  being  hinged,  so  when  the  load  W  is  applied  the 
frame  will  collapse,  as  indicated  by  the  dotted  lines.  It  has  no 
strength  to  resist  the  horizontal  force. 

Next  consider  the  rectangular  frame  as  shown  in  Fig.  178. 
The  corners  are  rigidly  connected.  When  the  load  W  is  applied, 
the  frame  tends  to  take  the  shape  indicated  by  the  dotted  lines.  In 
doing  so,  each  of  the  members  must  bend  into  reverse  curves.  Thus 
the  frame  offers  great  resistance  to  the  horizontal  force. 

When  a  member  is  bent  into  reverse  curves,  the  point  of  reversal 
is  called  the  "point  of  contraflexure"  There  is  no  bending  stress 
in  the  member  at  this  point  and  hinged  joints  might  be  introduced 
at  such  points  without  affecting  the  stability  of  the  frame  so  far  as 
the  horizontal  load  is  concerned.  This  is  indicated  in  Fig.  179. 
The  point  of  contraflexure  is  taken  at  the  middle  of  the  length  of 
each  member.  This  is  not  exactly  correct,  but  is  accurate  enough 
for  designing,  in  all  ordinary  cases. 

In  order  to  more  easily  understand  the  stresses  in  the  frame, 
consider  the  points  of  contraflexure  e,  f,  and  g  as  hinged  joints.. 
They  divide  the  frame  into'  four  parts  which  can  be  considered 
separately  in  determining  the  stresses.  Take  first  e  af,  and  assume 
the  horizontal  reactions  at  e  and  /  to  be  equal,  hence  each  is  \W. 
The  vertical  reactions  at  e  and  /  must  form  a  couple  which  will 
balance  the  moment  of  the  horizontal  loads,  hence,  taking  moments 
about  e, 


from  which  V  =  $W- 

LJ 

The   bending   moment   at  a  in  the   vertical  member    is  \\Vx\H, 
or  JTF/7;  and  in  the   horizontal   member  is   Vx\L  which  equals 

\  IV  II. 


Next  consider  the  part  e  c,  which  is  subjected  to  the  loads  \W 
and  V  applied  at  e.  The  reactions  at  o  are  the  same  in  amount  but 
opposite  in  direction,  To  maintain  equilibrium,  there  must  be  a 
couple  to  neutralize  the  moment  of  the  horizontal  force  at  e  about 
the  center  c.  This  couple  is  furnished  by  the  foundation  which  is 


248 


STEEL  CONSTRUCTION 


assumed  to  be  ample  to  resist  the  bending  moment  in  the  post  at  c, 

which  is 

1  WH 


In  like  manner  the  bending 
moments  at  b  and  d  can  be 
shown  to  be  J  WH.  Note  that 
the  numerical  value  of  the  bend- 
ing moment  is  the  same  at  the 
four  corners  of  the  frame.  The 
moment  diagram  is  given  in  Fig. 
180. 

In  addition  to  the  bending 
stresses  in  the  members,  there 
are  axial  stresses,  as  indicated 
by  the  forces  and  reactions  illus- 
trated: 
J  W,  compression 

TT 

V  —  ^W—t  compression 
Lt 

TJ 

in  a  c         V  =  %W  —  ,  tension 
L 

PROBLEM 

Refer  to  Fig.  179.  Assume  W  equals  10,000  pounds,  H  equals  16  feet, 
L  equals  20  feet.  Compute  the  axial  stresses  in  the  three  members  of  the  frame. 
Compute  the  bending  moment  at  a.  Construct  the  moment  diagram. 


Fig.  180.    Moment  Diagram  of  Single  Rec- 
tangular Panel 


in  a  b 
'mbd 


/[A 


Fig.  181.    Diagram  for  Two  Rectangular  Panels 


Two   Horizontal  Panels.     Next  consider  a  framework  of  two 
panels,  i.  e.,  made  of  three  columns  and  two  girders,  as  in  Fig.  181, 


STEEL  CONSTRUCTION 


249 


subjected  to  a  load  W.  It  is  necessary  to  assume  the  division  of 
the  horizontal  reactions  between  the  foundations  1,  2,  and  3.  Sev- 
eral different:  methods  are  used  in  practice.  It  is  not  of  much 
importance  which  is  used,  if  the  stresses  resulting  from  the  assumed 
divisions  are  adequately  provided  for.  In  this  text  it  is  assumed 
that  the  reactions  at  the  end  columns  are  one-half  of  those  at  the 
intermediate  columns.  Thus  the  reactions  at  /,  2,  and  8  are  J  W, 
\  H',  and  \  IV,  respectively.  By  reasoning  similar  to  that  used  for 
the  single  panel,  the  maximum  bending  moments  are  found  to  be: 

at  the  base  and  top  of  columns  /  and  3,          \  Wx%  II  - 
at  the  base  and  top  of  column    2, 
and  in  the  girders  to  the  right  of  a  and  61 
and  to  the  left  of  b  and  c,  / 

In  analyzing  this  case,  the  frame  niay  be  considered  as  made  up  of 
two  separate  panels,  each  of  which  carries  one-half  the  load  W. 


Fig.  182.     Moment  Diagram  for  Frame  of  Two  Rectangular  Panels 

Then  the  bending  moment  at  all  maximum  points  is  ^IV  II.  But 
column  2  is  common  to  both,  hence  its  total  stresses  are  the  algebraic 
sums  .of  the  stresses  from  the  two  panels.  As  the  bending  stresses 
are  of  the  same  sign,  the  bending  stresses  in  column  2  are  twice 
those  in  columns  1  and  3;  on  the  other  hand  the  axial  stresses  in 
column  2  are  opposite  in  sign  and  tend  to  neutralize  each  other. 
The  resultant  is  zero  if  L,  equals  Lr  The  moment  diagram  of  this 
case  is  given  in  Fig.  182. 

Horizontal  Row  of  Panels.  The  foregoing  method  now  can  be 
applied  to  a  frame  of  any  number  of  panels  The  total  horizontal 
load  or  shear  is  divided  by  the  number  of  panels.  Give  one  portion 


250 


STEEL  CONSTRUCTION 


to  each  of  the  intermediate  columns  and  one-half  portion  to  each 
of  the  outside  columns.     Thus  in  Fig.   183  there  are  five  panels. 


Fig.  183.     Diagram  Showing  Division  of  Shear  in  a  Frame  of  Five  Panels 


The  shear  is  distributed  thus:  —IF  at  columns  /  and  6,  and  <  W  at 
columns  #j#>-4>  and  tl.  The  bending  moments  in  columns  1  and  £are: 
—  WH't  in  columns  2^3,  4,  and  5,  —IF//;  and  in  all  girders,—-  W 11. 


Fig.  1S4.     Stresses  in  a  Two-Story  Rectangular  Framework 

PROBLEM 

•Assume  a  frame  of  7  panels,  supporting  a  wind  load  of  115,000  pounds. 
Let  H  equal  14  feet.  Compute  the  maximum  bending  moments  and  draw  the 
moment  diagram. 

Two^Story  Framework.  Next  assume  the  case  illustrated  in 
Fig.  184.  This  shows  the  framework  of  a  two-story  building.  The 
points  of  contraflexure  occur  at  the  points  indicated  by  the  black 
dots.  The  loads  applied  are  WB  at  the  roof  and  IF2  at  the  second 


STEEL  CONSTRUCTION  251 

floor.    The  first-story  frame  serves  as  a  foundation  for  the  second- 
story  frame.    The  horizontal  shears  which  are  transmitted  through 

the  points  of  contraflexure  in  the  second-story  columns  are  -  WR 

and  -  WR  as  indicated;  those  transmitted  through  the  points  of 
o 

contraflexure  in  the  first-story  columns  are  -   (WR+WJ  and  - 

^6  3 

(WR+IV2)  as   shown.    The   vertical   shears    transmitted   through 

points  of  contraflexure  in  the  roof  girders  are  F«  = —-,  and 

6      L 

those  transmitted  through  the  second-floor  girders  are 

v  _1  WRH2+(WR+W2)Ht 
K~  ~~~ 


(assuming  panels  of  equal  length).    Then  the  bending  moments  are 

.  at  a  in  roof  girders  ~~TzWRH- 

12 

at  b  in  2nd  floor  girder        -™  [WRH2+(WR+WJ  HJ 

at  c  in  columns  +—  WRHt 

12 

at  d  in  columns  +—WRH2 

\ 

at  e  in  columns  H — -  (Wn+W.)  H. 

12 

at/  in  columns  +—  (WR+WJ  Hl 

An  important  relation  to  be  noted  is  that  at  any  joint  the  sum  of 
the  moments  in  the  members  equals  zero,  or  the  sum  of  the  moments 
in  the  column  equals  the  sum  of  the  moment  in  the  girders.  Thus 
at  column  1,  2nd  floor 


«t  l-R 

at  column  2,  2nd  floor 

1  (WR+WJ  J7.-2X  ^5  [WBH,+(WS+W,)  H,] 

O  1Z 


252 


STEEL  CONSTRUCTION 


Extension  of  System  in  Either  Direction.  The  method  can  now 
be  applied  to  a  frame  of  any  extent,  vertically  and  horizontally. 
Fig.  185  shows  such  a  frame  six  panels  in  width  and  six  stories  and 
basement  in  height.  The  loads  applied  at  the  several  floor  levels 
are  represented  by  Wv  W2  ....  WR.  The  total  shears  in  the 
several  stories  are  represented  by  WJ,  WJ,  W2' W6'. 


Fig.  185.     Diagram  of  Wind  Stresses  in  a  Building  Frame 

The  total  shear  in  any  story  is  the  sum  of  all  the  loads  applied  at  the 
floors  above,  thus, 


The  total  shear  in  any  story  is  divided  between  the  columns  in  that 
story  in  accordance  with  the  rule  given.  This  is  illustrated  in  the 
figure  by  the  values  given  in  the  first  story. 


STEEL  CONSTRUCTION  253 

The  bending  moments  are  illustrated  at  the  third  floor  in  the 
figure  and  the  moments  diagrams  at  the  fifth  floor. 

The  procedure  can  now  be  reduced  to  simple  rules  and  formulas. 

The  bending  moment  in  an  intermediate  column  .in  any  story 
equals  the  total  shear  in  that  story  multiplied  by  the  story  height,  and 
the  product  divided  by  two  times  the  number  of  panels.  This  is 
expressed  by  the  formula 

«•* 

The  bending  moment  in  an  outside  column  is  one-half  that  in  an 
intermediate  column,  or, 

«^f 

The  bending  moment  in  a  girder  is  the  mean  between  the  bending 
moments  in  the  column  above  and  below  the  girder.  It  is  expressed  by 
the  formula 


NOTE,  a  and  b  refer  to  two  adjacent  stories,  as  the  third  and  fourth.  The 
panel  length  does  not  affect  the  value  of  the  bending  moment. 

Illustrative  Example.  Compute  the  bending  moments  at  the 
first  floor  in  the  frame  in  Fig.  185.  Assume  that  the  loads  applied 
above  the  first  story  sum  a  total  of  66,000  pounds  equal  WJ,  those 
above  the  basement  story  a  total  of  75,000  pounds  equal  WB'> 
Let  HB  equal  10  feet,  and  Hl  equal  16  feet.  Then  the  bending 
moment  is: 

in  an  intermediate  basement  column 
75,000X10 


2X6 

in  the  intermediate  first-story  columns 
66,000X16 


62,500  ft.-lb. 


2X6 
in  the  first-floor  girders 


88,000  ft-lb. 


Axial  Stresses.  The  axial  stresses  may  be  disregarded  in  most 
cases.  They  are  usually  small  in  proportion  to  the  sections  otherwise 
required  for  the  members.  The  girders  may  be  considered  as  being 


254 


STEEL  CONSTRUCTION 


relieved  from  this  stress  by  the  floor  construction.  If  there  be  no  floor 
construction  along  the  girders,  the  axial  stress  should  be  considered. 
In  the  intermediate  columns  the  axial  stress  is  zero  if  the  panel 


-L- 


Fig.  1S6.     Diagram  of  Overturning  Stresses  in  a  Building  Frame 

lengths  are  equal.  In  the  outside  columns  the  axial  stress  occurs, 
but  here  the  bending  moment  is  only  one-half  that  in  the  intermedi- 
ate columns,  so  the  axial  stress  is  usually  not  important;  however, 
in  tall,  narrow  buildings  it  may  be  important  and  should  be  com- 
puted. When  required,  it  can  be  computed  thus:  In  Fig.  186  the 
arrows  represent  the  wind  pressure  on  the  framework  shown.  The 


STEEL  CONSTRUCTION  255 

resultant  .of  this  pressure  is  W,  acting  at  mid-height  of  the  exposed 
part  of  the  structure.  The  axial  stress  V  in  the  basement  section 
of  the  end  column  is  found  by  taking  moments  about  the  point  B. 
The  stress  in  the  first-story  section  is  found  by  taking  moments 
about  the  point  1. 

PROBLEMS 

1.  Assign  values  to  the  structure  illustrated  in  Fig.  186  and  compute  the 
axial  stress  in  the  second-story  sections  of  the  end  columns. 

2.  In  Fig.  185  assume  the  following  values: 

HB  =  lO'-O" 

Hi  =16'-6* 

//2,//3---ffo=12'-6* 
W,  =  8,000# 

W2  =14,500# 


WR  =  10,000# 

(a)  Compute  WB',  W,'t  -----  Wu'. 

(b)  Compute  the  maximum   bending  moment  for  an  interior  column 
above  and  below  each  floor  line. 

(c)  Compute  the  maximum  bending  moment  in  the  girders  at  each  floor. 

(d)  What  is  the  bending  moment  in  the  second-floor  girder  at  a  point 
l'-9"  to  the  right  of  column  4? 

(e)  Construct  the  moment  diagram  for  column  7  from  basement  floor  10 
roof. 

DESIGN  OF  WIND-BRACING  GIRDERS 

In  the  preceding  pages  the  method  has  been  developed  for 
determining  the  bending  moments  in  wind-bracing  girders  and 
columns.  It  has  been  shown  that  the  maximum  bending  moment 
occurs  at  the  intersection  of  the  column  and  the  girder,  and  zero 
moment  occurs  at  the  center  of  the  girder.  Between  these  points 
the  moment  varies  uniformly,  as  shown  by  the  moment  diagrams  in 
Figs.  180,  182,  and  185.  By  laying  out  the  moment  diagram  to 
scale,  the  bending  moment  at  any  point  may  be  measured. 

End  Connections  for  Riveted  Girders.  Heretofore  in  designing 
beams,  end  connections  have  been  required  to  resist  only  vertical 
shear,  but  in  the  case  of  wind-bracing  girders  it  is  evident  that  the 
connection  of  the  girders  to  the  column  is  chiefly  to  resist  the  bending 
moment.  This  connection  requires  careful  designing  to  insure 
effective  results. 

To  illustrate  the  design,  assume  an  example  as  follows:  In 
Fig.  187  the  distance  center  to  center  of  columns  is  20  feet;  the  max- 


cp  0 


(ASSUM 

•\LINES  IN  GUSSET  PLT. 


O    (p    0 


Fig.  187.     Design  of  a  Wind  Bracing  Girder 


STEEL  CONSTRUCTION  257 

imum  bending  moment  is  400,000  foot-pounds  or  4,800,000  inch- 
pounds;  the  depth  of  girder  is  3  feet  \  inch  back  to  back  of  angles. 
As  stated  on  page  51,  the  unit  stresses  to  be  used  are  fifty  per  cent 
in  excess  of  those  allowed  for  gravity  loads. 

The  girder  connects  to  the  web  of  the  column.  As  the  end  of 
the  girder  thus  lacks  only  about  an  inch  of  reaching  to  the  column 
center,  the  maximum  bending  moment  must  be  provided  for,  viz, 
4,800,000  inch-pounds. 

Rivets  Connecting  Girder  to  Column.  The  rivets  through  the 
end  angles  and  column  webs  are  field  driven,  |  inch  diameter,  and 
on  the  tension  side  of  the  girder  (above  the  neutral  axis  in  this  case) 
are  in  tension,  As  in  a  beam,  the  unit  fiber  stress  varies  from  zero 
at  the  neutral  axis  to  a  maximum  at  the  extreme  fiber;  so  the  unit 
stress'  in  these  rivets  varies  from  zero  at  the  neutral  axis  to  the  max- 
imum allowable  amount  at  the  farthest  rivet. 

Then,  if  the  rivets  are  equally  spaced,  the  average  stress  is 
one-half  the  maximum.  The  total  resistance  of  the  rivets  is  the 
average  value  of  one  rivet  multiplied  by  the  number  of  rivets  in  the 
tension  (or  compression)  group  represented  by  t  (and  c);  the  centers 
of  gravity  of  the  groups  are  at  the  points  t  and  c.  The  moment  arm 
is  the  distance  a  between  t  and  c,  and  the  resisting  moment  is  aXt 
(or  c).*  The  number  of  rivets  required  is  determined  by  trial.  The 
full  value  of  a  J-inch  rivet,  field  driven,  in  tension  is  one  and  one- 
half  times  6000  pounds  or  9000  pounds.  Several  trials  lead  to  the 
use  of  28  rivets  on  each  side  of  the  neutral  axis.  The  value  of  t  is 

9000  X  28 

-  or  126,000  pounds.    The  moment  arm  a  is  42  inches  and 

2i 

the  resisting  moment  of  the  joint  is  126,000X42  or  5,292,000  inch- 
pounds,  which  is  about  ten  per  cent  in  excess  of  the  bending  moment. 

PROBLEM 

Design  the  above  joint,  using  f-inch  rivets  spaced  2|  inches. 

Rivets  Connecting  End  Angles  to  Gusset  Plate.  Now  consider  the 
rivets  connecting  the  end  angles  to  the  gusset  plate.  The  method 
is  the  same  as  that  for  the  connections  of  the  end  angles  to  the 
column,  except  that  the  rivets  are  shop  driven  in  double  shear. 

This  is  not  exact,  for  the  rivets  on  the  compression  side  do  not  act,  the  compression  being 
resisted  by  the  direct  bearing  of  the  end  of  the  girder  against  the  column.  The  error  is  on  tho 
safe  aide 


258  STEEL  CONSTRUCTION 

The  required  results  can  easily  be  obtained  by  comparison  with 
field-driven  rivets.  With  one  row  of  rivets  there  will  be  one-half 
as  many  (less  one).  One  shop  rivet  in  double  shear  is  good  for 
21,600  pounds.  This  is  greater  than  the  value  of  two  rivets  in  ten- 
sion (18,000  pounds),  hence  the  proposed  arrangement  is  satis- 
factory. It  gives  greater  strength  than  is  required. 

The  thickness  of  gusset  plate  required  to  develop  the  full 
shearing  value  of  the  rivets  is  H  inch.  The  thickness  required  for  the 
actual  stress  is  ft  inch,  which  use.  (See  rivet  tables  in  handbook.) 

PROBLEM 

What  thickness  of  gusset  plate  is  required  for  f-inch  shop  rivrts? 

Bending  Stresses  in  Connecting  Angles.  No  accurate  determi- 
nation can  be  made  of  bending  stresses  in  connecting  angles,  so 
thickness  must,  be  adopted  arbitrarily.  If  the  gage  line  of  the 
rivets  is  not  more  than  2J  inches  from  the  back  of  the  angle,  the 
thickness  should  be  f  inch.  In  many  cases  wide  angles  with  large 
gage  distance  must  be  used  in  order  to  match  the  gage  lines  in  the 
.  column.  A  thickness  of  1  inch  seems  to  be  safe  for  a  gage  distance 
of  4  inches.  Intermediate  values  may  be  interpolated. 

Gusset  Plate.  The  slope  of  the  gusset  plate  should  be  about 
45  degrees,  but  may  vary  to  suit  conditions,  such  as  clearance 
from  windows,  etc.  Stresses  in  the  gusset  plate  may  be  imagined  to 
act  along  the  dotted  lines  shown  in  the  figure.  On  the  tension  side 
of  the  girder  the  plate  is  in  tension,  and  on  the  compression  side  in 
compression.  The  thickness  of  plate  required  for  rivet  bearing  is 
sufficient  to  give  the  necessary  strength  on  the  tension  side,  but  on 
the  compression  side  stiffener  angles  may  be  required.  These 
angles  can  be  designed  according  to  rules  similar  to  those  given  for 
the  stiffeners  of  plate  girder  webs,  p.  148.  They  should  be  used 
when  the  length  of  the  diagonal  edge  of  the  plate  is  more  than 
thirty  times  the  thickness.  The  leg  of  the  angle  against  the  plate 
should  be  of  suitable  width  for  one  row  of  rivets,  say  3  inches,  3| 
inches,  or  4  inches.  The  outstanding  leg  may  vary  from  3  to  6 
inches.  A  thickness  of  -J-  inch  is  suitable  usually;  it  may  be  made 
more  or  less  to  be  consistent  with  size  and  thickness  of  the  main 
members  of  girder.  For  the  case  illustrated  use  2Ls  SV'XS^'X »". 

Girder  Section.  The  critical  section  of  the  main  girder  is  at 
the  end  of  the  gusset  plate  (because  there  arc  no  gravity  loads).  The 


STEEL  CONSTRUCTION 


259 


WEB   PL  A  TE    Of 
CMD  ANGLES  OF  Gl 


plate  being  2'-(i"  wide,  the  bending  moment  at  this  point,  as 
<letmnii)e<i  from  the  moment  diagram,  is  ; {00,000  foot-pounds,  or 
;5,(i()0,000  inch-pounds,  Fig.  1ST. 

It  is  usually  economical  to  make  the  girder  as  deep  as  condi- 
tions will  permit.  In  most  cases  it  is  limited  by  the  windows  above 
and  below.  For  this  ca^c  M'-OV'  back  to  back  of  angles  is  assumed. 

The  sedion  is  determined  by  the  methods  given  for  riveted 
girders,  p.  Ill,  using  the  increased  unit  stresses  previously  men- 
tioned. Note  that  the  web  is  spliced  at  the  point  under  consid- 
eration. 

The  spacing  of  rivets  that  connect  the  flange  angles  to  the  web 
plate  is  determined  as  in  riveted  girders,  p.  149.  As  the  bending 
moment  varies  uniformly  from  the  center  to  the  end,  the  rivets  are 
equally  spaced.  This  spacing  may  be  continued  for  connecting 
the  flange  angles  to  the  gusset  plate.  But  there  must  be  enough 
rivets  through  the  gusset  plate  to  transmit  all  of  the  stress  which 
is  in  the  flange  angles  at  the  edge  of  the 
gusset.  Connecting  angles  may  be  needed 
ist  in  connecting  the  flange  angles 
to  the  gusset  plate. 
PROBLEMS 

1.  Design  UK    girder  section,  flange  rivet- 
ing, and  web  splice,  Fig.  187. 

2.  Make  drawing  at  1-iwh  scale  showing 
side  elevation,  end  elevation,  and   section  of  the 
fMrd'i.    (l'.-e  the  design  with  ;[-ine,h  rivets.)    Show 
rivet  spacing. 

Other  Forms  of  End  Connections.  Fig.  188  shows  a  girder  con- 
nection differing  from  the  previous  case  in  that  the  column  is  turned 
in  the  other  direction.  The  connection  is  designed  in  just  the  same 
manner  but  the  amount  of  the  bending  moment  is  somewhat  less 
than  the  maximum  because  it  is  some  distance  away  from  the  center 
of  the  column.  The  actual  amount  can  be  computed  or  scaled  from 
the  moment  diagram. 

PROBLEM 

What  is  the  bending  moment  at  the  end  of  th»-  girder  shown  in  Fig.  1SS, 
the  moment  at  the  center  of  the  column  being  400,000  foot-pounds  and  t he- 
distance,  center  to  center  of  columns,  10  f«i7 

In  Fig.  189  the  web  of  the  girder  connects  directly  to  the  flange 
of  the  column.  This  form  of  connection  is  suitable  for  girders  which 


Fig.  188       Section  of 

of  Girder  to  Colurnu 


260 


STEEL  CONSTRUCTION 


are  deep  in  proportion  to  the  bending  moment  which  they  must 
resist.  The  method  of  designing  the  connection  is  the  same  as  that 
explained  for  Fig.  187,  except  that  the  rivets  are  in  single  shear  in- 
stead of  tension,  and  that  the  rivets  are  not  evenly  spaced,  hence 
the  average  resistance  may  not  be  one-half  the  maximum.  The 
value  of  each  rivet  can  be  measured  from  the  diagram  at  m  in  the 


Fig.  1S9.     Details  of  Connection  of  Girder  Directly  to  the  Face  of  the  Column 

figure.    Having  the  values  of  the  several  rivets,  the  center  of  gravity 
of  each  group,  i.  e.,  the  positions  of  the  resultants  t  and  c,  can  be 
found  in  the  usual  way. 
PROBLEM 

Compute  thejesisting  moment  of  the  connection  shown  in  Fig.  189.  Use 
f-inch  rivets,  and  assign  suitable  spacing  for  them.  Design  the  girder  section 
corresponding  to  this  resisting  moment. 

When  the  form  of  connection  shown  in  Fig.  189  is  not- ade- 
quate, the  gusset  plate  can  be  used  connecting  directly  to  the  flange 
of  the  column.  It  involves  no  principles  or  methods  different  from 
those  already  explained. 


STEEL  CONSTRUCTION 


261 


End  Connections  for  I -Beam  Girders.     I-beam  connections  for 
resisting  bending  are  illustrated  in  Figs.  190,  191,  and  192. 


Fig.  190.     Connection  of  I-Bcam  to  Flangi 
of  Column  For  Wind  Bracing 


ickct  Connection  of  I-Beam  for 
Wind  Bracing 


VETS* 


Fig.  191.     Connection  of  I-Beam  to  Side  of 
Column  for  Wind  Bracing 


The  detail  in  Fig.  190  is 
similar  to  the  connection  shown 
in  Fig.  189.  It  can  develop 
only  a  small  part  of  the  capa- 
city of  the  beam. 

The  detail  in  Fig.  191  also 
can  develop  only  a  part  of  the 
capacity  of  the  beam,  but  it  is 
available  for  making  use  of  the 
floor  girders  in  the  upper  part 
of  the  building  for  resisting 
wind  stresses.  The  strength 
of  this  connection  is  limited 
by  the  bending  resistance  of 
the  connecting  angles  or  the 
strength  of  the  rivets. 

PROBLEM 

Compute  the  bending  resist- 
ance of  the  connection  shown  in 
Fig.  191. 

Bracket  Connection.  The 
connection  in  Fig.  192  can  be 
made  to  develop  the  entire  net 
bending  resistance  of  the  beam 


262 


STEEL  CONSTRUCTION 


(deducting  for  rivet  holes  in  the  flanges).  The  connection  of  the 
brackets  to  the  column  is  designed  in  the  same  manner  as  described 
for  the  gusset  plate  connection.  The  average  value  of  the  rivets  is 
determined  from  the  diagram  as  at  m.  Fig.  189.  In  the  connection  of 
the  brackets  to  the  beam,  all  the  rivets  are  figured  at  the  maximum 
value.  Their  resisting  moment  is  their  total  shear  value  multiplied 
by  the  depth  of  the  beam. 

PROBLEM 

Design  a  bracket  connection  that  will  develop  the  net  bending  resistance 
of  a  24"  I  80#. 

COMBINED  WIND  AND  GRAVITY  STRESSES  IN  GIRDERS 

The  girders  which  are  usually  used  to  resist  wind  stresses  are 
also  subjected  to  gravity  stresses  in  supporting  walls  and  floors. 
It  is  necessary,  therefore,  to  determine  the  combined  effect  before 
the  member  can  be  designed. 

Moment  Diagram  for  a  Restrained  Beam.  In  the  discussion  of 
beams,  it  was  considered  that  the  ends  rested  freely  on  the  supports. 

With  these  conditions  the  beam 
under  a  gravity  load  tends  to 
deflect  in  the  form  of  a  simple 
curve  and  its  moment  diagram 
lies  entirely  below  the  axis  o-o, 
Fig.  193-a.  If  the  beam  is  re- 
strained by  rigid  connections  at 
the  ends,  as  illustrated  in  Fig. 
192,  it  tends  to  deflect  in  the 
form  of  a  compound  curve  and 
the  moment  diagram,  Fig.l93-b, 
lies  both  above  and  below  the 
axis.  The  part  of  the  diagram 
above  the  axis  represents  nega- 
tive moment  and  the  part  below, 

positive  moment.  The  total  depth  of  the  moment  diagram  is  \  W  L 
(for  a  uniformly  distributed  load)  in  each  case. 

Positive  and  Negative  Moments.  The  division  of  the  moment 
diagram  of  a  restrained  beam  between  positive  and  negative  moments 
depends  on  a  number  of  conditions.  The  conditions  usually  assumed 
as  ideal  are  that  the  beam  is  of  constant  cross  section  from  end  to 


Fig.  193.     Moment  Diagrams  (a)  of  Sii 
Beam;  (b)  of  Restrained  Beam 


iple 


STEEL  CONSTRUCTION  263 

end  and  that  the  end  connections  are  absolutely  rigid.    Then  the 

bending  moment  at  the  ends  is  —  —  W  L,  and  at  the  middle  is 

12 

+*WL- 

If  the  section  of  the  beam  at  mid-span  is  less  than  at  the  ends, 
as  is  the  case  when  the  connections  are  made  by  deep  gusset  plates 
or  brackets,  the  positive  moment  is  less  and  the  negative  moment 
greater  than  the  above  values.  The  extreme  case  would  be  when  a 
beam  had  no  bending  resistance  at  the  center  (as  if  hinged),  in  which 
case  the  two  halves  would  act  as  cantilevers;  there  would  be  no 
positive  moment  and  the  negative  moment  would  equal  J  W  L 
(W  being  the  total  load  on  the  span). 

The  assumed  ideal  condition  of  absolute  rigidity  at  the  ends 
is  not  realized  because  the  columns  must  deflect  laterally  under 
load.  This  lack  of  absolute  rigidity  tends  to  decrease  the  negative 
moment  and  to  increase  the  positive  moment.  The  same  effect  is 
produced  if  the  connection  is  not  sufficient  to  develop  the  strength 
of  the  beam  section,  as  in  the  examples  shown  in  Figs.  190  and  191. 
In  the  extreme  case  when  the  columns  or  the  connections  are  ex- 
tremely weak  in  bending  resistance,  the  negative  moment  approaches 
zero  and  the  positive  moment  approaches  J  W  L. 

It  is  not  practicable  to  determine  definitely  the  amount  of 
negative  and  positive  moments  for  a  given  case,  so  arbitrary  values 
must  be  adopted.  The  designer  generally  should  assume  that  the 

moments  from  the  gravity  loads  are  —  —  WL  at  the  ends  and 

\.2t 

+—  WL  at  mid-span,  and  should  design  the  end  connections  and 

fn 

the  beam  section  accordingly.  But  a  less  value  may  be  used  at 
the  ends  and  a  corresponding  greater  value  at  the  center  if  it  is 
not  possible  to  make  end  connections  strong  enough  to  resist  the 
larger  value. 

Bending  Moments  for  Combined  Loads.  Now  consider  the 
bending  moments  resulting  from  the  combined  action  of  gravity 
and  wind  loads.  In  Fig.  194,  let  a  be  the  moment  diagram  for  a 
wind  load  and  Jb  the  moment  diagram  for  a  gravity  load.  Then  the 
total  effect  is  represented  by  c,  which  is  the  moment  diagram  for 


Fig.  194.     Moment  Diagrams  for  Combined  Loads 
(a)     Wind  Load  (b)  Gravity  Load 

(c)  Combined  Wind  and  Gravity  Loarls 

(d)  Maximum  Bending  Moment  Diagram 


STEEL  CONSTRUCTION  265 

the  combined  loads.  This  moment  diagram  c  is  constructed  by 
adding  together  the  moments  used  in  constructing  the  diagrams  a 
and  6. 

End  Connections  Designed  to  Resist  Wind  Loads.  Diagram  c, 
Fig.  194  shows  a  very  large  resultant  negative  bending  moment  at 
the  left  end  of  the  diagram,  and  a  very  small  resultant  positive 
bending  moment  at  the  right  end.  If  the  respective  end  connec- 
tions be  designed  to  resist  these  moments,  i.  e.,  the  left  end  with  a 
very  heavy  connection  and  the  right  end  with  a  very  light  connection 
(in  this  case  practically  a  hinged  joint),  then  the  distribution  of 
stresses  probably  would  be  as  represented  in  diagram  c.  But,  since 
the  wind  may  act  from  either  direction,  the  two  end  connections 
are  made  alike;  the  columns  at  the  two  ends  are  probably  of  about 
equal  size  and  stiffness;  then  it  is  reasonable  to  assume  that  the 
deflections,  and  hence  the  resistance  developed  at  the  two  ends,  will 
be  equal. 

For  this  condition  it  is  evident  that  diagram  c  does  not  repre- 
sent the  actual  distribution  of  moments.  To  have  a  diagram  which 
will  represent  it,  the  curve  must  be  shifted  so  that  the  negative 
moment  at  the  left. end  equals  the  positive  moment  at  the  right  end. 
This  gives  diagram  d.  The  same  diagram  results  directly  by  com- 
bining diagram  a  of  Fig.  193  with  diagram  a  of  Fig.  194.  It  will  be 
noted  that  the  bending  moments  at  the  ends  equal  the  bending 
moments  from  the  wind  loads.  Hence,  the  end  connections  in.  all 
cases  are  designed  to  resist  the  wind  load  moments. 

Maximum  Bending  Moment.  The  bending  moment  at  the 
center  of  the  span  equals  the  bending  moment  of  the  gravity  load 
computed  for  an  unrestrained  beam.  However,  the  maximum  posi- 
tive bending  is  not  at  the  center,  but  some  distance  to  one  side  (to 
the  right  in  this  case)  and  its  amount  can  be  determined  by  con- 
structing the  diagram  d.  The  value  thus  determined  governs  the  cross 
section  of  the  girder. 

As  has  been  stated,  the  unit  stresses  allowed  for  the  combined 
loads  are  50  per  cent  larger  than  those  for  the  gravity  load  alone.  The 
resulting  section  designed  for  the  maximum  positive  bending  moment 
from  diagram  d  will  always  be  larger  than  the  section  required  by 
the  negative  moment  of  gravity  load  from  diagram  b  and  more  than 
twice  the  section  required  by  the  maximum  positive  bending  moment 


266 


STEEL  CONSTRUCTION 


from  diagram  b,  diagram  b  being  tne  moment  diagram  for  the  gravity 
loads  on  a  restrained  beam,  when  the  wind  is  not  acting.  Note, 
however,  that  the  section  required  is  less  than  would  be  required 
for  the  gravity  load  on  a  simple  (unrestrained)  beam,  diagram  a, 
Fig.  193. 

PROBLEMS 

1.  In  Fig.  194  assume  values  given  for  diagrams  a  and  b.     Determine  the 
maximum  positive  and  negative  values  for  diagram  d.     Construct  diagram  d 
accurately  to  scale. 

2.  Design  a  girder  of  the  type  shown  in  Fig.  187  from  the  moment  dia- 
gram d  in  Fig.  194. 

EFFECT  OF  WIND  STRESSES  ON  COLUMNS 

Combined  Direct  and  Bending  Stresses.    The  bending  moment 
on  the  column  due  to  wind  loads  produces  the  same  sort  of  stresses 
I  as  result  from  the  bending  moment  due  to  eccentric 

loads  or  any  other  cause  producing  flexure.    The  ex- 
treme fiber  stress  is  computed  from  the  formula 


This  stress  is  added  to  the  stresses  resulting  from  the 
direct  and  eccentric  loads  on  the  column  to  give  the 
maximum  fiber  stress. 

The  combination  of  the  direct  and  the  bending 
stress  is  illustrated  in  Fig.  195.  The  stress  from  the 
direct  -load  is  represented  by  the  rectangle  abed  and 
the  unit  stress  by  a  b.  The  stress  from  bending  is  rep- 
resented by  the  triangles  b  b'o  and  c  c'o,  the  extreme 
fiber  stress  being  b  br  in  compression  and  c  cf  in  tension.  Then  the 
maximum  fiber  stress  is  on  the  compression  side  and  is  ab+bb'. 
Thus  b  b'  represents  the  increase  in  stress  due  to  the  wind  load. 
If,  as  is  usually  the  case,  b  b'  amounts  to  less  than  half  a  b,  the 
column  section  required  for  the  direct  load  need  not  be  increased  on 
account  of  the  wind  stress,  because  of  the  increased  units  allowed 
for  combined  stress.  But  if  b  b'  exceeds  one-half  of  a  b,  the  combined 
stress  will  govern  the  design  using  the  increased  unit  stress. 

On  the  tension  side  of  the  column,  the  wind  stress  will  very 
rarely  be  great  enough  to  overcome  the  direct  compression.    And 


Fig.  195.  Dia- 
gram of  Com- 
bined and  Di- 


STEEL CONSTRUCTION 


267 


if  there  should  be  a  reversal  of  stress,  there  cannot  be  tension  enough 
to  require  any  addition  to  the  section.  It  frequently  occurs  that 
the  wind  bracing  girder  connects  to  the  column  in  such  a  position 
that  one  side  of  the  column  must  resist  practically  all  the  wind 
stress.  Such  a  case  is  illustrated  in  Fig.  189.  With  these  condi- 
tions only  one-half  the  column  section  should  be  used  in  computing 
the  resulting  extreme  fiber  stress. 

Design  of  Column  for  Combined  Stresses.  The  procedure  in 
designing  the  column  section,  when  the  combined  wind  and  gravity 
loads  govern,  is  the  same  as  has  been  given  for  columns  with  eccen- 
tric loads,  p.  174.  The  method  there  given  for  computing  the  con- 

centric equivalent  load  also  applies,  as  well  as  the  formula 

« 

Ww'  =  W'—2 
r 

As  applied  to  wind  load  (refer  to  Fig.  196)  Ww'  is  the  equivalent 

concentric  load,  i.  e.,  the  direct  ^ 

load  that  would  produce  the 

same  unit  stress;  W  is  the  hor- 

izontal shear  which  is  assumed 

to  be  carried  by  the  column 

under  consideration  and  is  as- 

sumed to  be  applied  at  the 

point  of  contraflexure  of  the 

column  (see  Fig.  185);  e  is  the 

moment    arm     expressed    in 

inches,  hence  We  is  the  bend- 

ing moment  in  inch-pounds  at 

the  section  under  considera- 

tion;  c  is  the  distance  from 

the  neutral  axis  of  the  column 

to  the  extreme  fiber  on  the 


JO.  000*\ 


t 


POINT  OF  C0/YT/TA, 
-FLEXURE 


'HEAR  FROM  U D 

Vfviwrr  LOAD 


is'-o  c  TO  c  OF 


COLUMNS 

Cw!-/5ooo* 


Fig.  196.     Details  of  a  Problem  in  Wind  Bracing 


compression  side;  r  is  the  radius  of  gyration  of  the  column  in 
the  direction  under  consideration.  The  critical  section  of  the 
column  is  at  the  top  of  the  bracket,  as  the  bracket  has  the  effect 
of  enlarging  the  column  section,  so  the  distance  e  is  measured  to 
that  point. 

To  illustrate  the  use  of  the  formula  assume  the  following  data: 


268  STEEL  CONSTRUCTION 

Direct  or  gravity  load  on  column  is  600,000  pounds;  W  is  10,000 
pounds",  e  is  30  inches;  c  is  7  inches;  and  r  is  3.5  inches.    Then 


As  this  is  less  than  half  the  gravity  load  it  is  neglected 

PROBLEM 

In  Fig.  196  are  given  the  essential  dimensions  and  the  loads  on  the  columns 
in  the  first  and  second  story  of  a  building  and  the  girders  at  the  second  floor. 

(a)  Design  the  columns  and  girders. 

(b)  Write  a  complete  record  of  all  computations. 

(c)  Make  a  drawing  of  the  joint  at  f-inch  scaje. 


FORT  DEARBORN  HOTEL,  CHICAGO 
Holabird  &  Roche,  Architects 


STEEL  CONSTRUCTION 

PART  IV 


PRACTICAL  DESIGN 

SIXTEEN=STORY  FIREPROOF  HOTEL 

Having  studied  the  stresses  and  the  design  of  individual  steel 
members,  attention  will  now  be  given  to  the  problems  which  arise  in 
the  design  of  the  structural  framework 'of  a  building. 

It  is  assumed  that  the  student  now  understands  how  to  com- 
pute stresses  and  how  to  design  individual  members  of  the  frame- 
work; therefore,  detailed  computations  of  these  operations  in 
most  cases  are  not  given.  Nor  are  references  given  to  the  preceding 
parts  of  the  work,  except  in  a  few  cases,  it  being  left  to  the  student 
to  seek  these  references  for  himself  if  he  needs  them.  This  applies 
also  to  the  tables  and  diagrams  in  this  book  and  in  the  handbooks. 

Description  of  Building*.  The  building  selected  for  the  purpose 
of  illustrating  the  practical  problems  of  design  has  been  taken 
because  it  gives  an  unusually  large  number  of  special  conditions. 
For  this  reason  it  cannot  be  considered  as  a  typical  case.  Its  fram- 
ing differs  from  that  most  commonly  seen  in  buildings  because 
steel  joists  are  not  used. 

The  building  is  designed  to  be  used  as  a  hotel.  It  has  sixteen 
stories  and  an  attic  above  street  level  and  a  basement  below  street 
level.  It  also  has  a  sub-basement  over  part  of  the  area  to  provide 
space  for  a  power  plant.  The  basement  extends  under  the  sidewalk 
on  two  sides  of  the  building. 

The  building  occupies  the  entire  lot,  except  for  a  light  court 
above  the  third-floor  level.  Fireproof  construction  is  used  through- 
out. The  framework  consists  of  structural  steel  columns  and 
girders.  The  floor  construction  consists  of  reinforced  concrete 
slabs  and  joists,  with  tile  fillers  between  the  joists.  In  most  of  the 

•The  Fort  Dearborn  Hotel,  Chicago,  Illinois;  Holabird  and  Roche,  Architects. 


270  STEEL  CONSTRUCTION 

building  the  concrete  slabs  form  the  finished  floor.  Partitions  in 
general  are  three-inch  hollow  tile,  plastered  on  both  sides.  They 
are  fixed  in  position  (this  has  some  bearing  on  the  arrangement  of 
girders).  The  foundations  are  cylindrical  concrete  piers  extending 
to  rock.  The  basement  walls  are  of  reinforced  concrete.  The  walls 
above  grade  are  brick'  with  terra  cotta  trimmings. 

Plates  A  to  X  give  the  complete  structural  framing  plans,  and 
a  part  of  the  architectural  floor  plans  and  elevations,  which  are 
sufficient  for  this  problem;  but  additional  architectural  details 
would  be  required  for  making  the  complete  design. 


J, 


fOUHPATIOH   PLAN. 

Plate  A.     Foundation  Plan,  Fort  Dearborn  Hotel 
Courtesy,  Uolabird  &  Roche,  Architects 


Plate  B.    Basement  and  Sub-Basement  Plans,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


\CONN.  TO    COLL/HNS  7-42  ^-          HANGER  BETWEEN 
III  FLOOR.  COL.  30  I.  37. 

STffUT   BET  WEE fi    • 

COL.?  9  I.  JO  BRACKETS  ON    COL  UMNS^-7  A/4-JS 

MOTE    JEE   PETAIL    OF    .STRUT  FOX    SUPPORTING     GRAH1TE   PIERS. 

MKP.'S  -4N  PLHTE     I  y/)X,;x  I&2-FLOOR. 


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f/fi vat, on  vfi, 
Side  walk  /j'  13-11" 


FIRS  7  FLOOR  FRAMING  PL  AN. 

Plate  C.     First  Floor  Framing  Plan  and  Details  of  Beam  Connections,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


GUSSET  PLT 


SPANPREL    CONNECTIONS     TO    COLUMNS  8-29 

f££- FLOOR.  5PAHPREL     CONNECTIONS    TO    COLUMNS  14 -, 

ZZP  FLOOR. 


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Z-5X3~xfx4-C~Lf  over  doo 
open  in y.  Col  ^3  -  36  -  fffe 


CONNECTION  TO  COLUMN J6 


Plate  D.     Second  Floor  Framing  Plan  and  Spandrel  Connections,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


:^ 


3V< 
.  ££ 


> 

s 


;? 


•ff rackets  about  4'- O  C.-C. 


97-6 


3*£-  FLOOR    FRAMING  PLAN. 

Plate  E.     Third  Floor  Framing  Plan  and  Spandrel  Sections,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


Tops  of  interior  beams  are  5$  belout  finished  floor-id  Ft. 
"      i       5." tG/tf. 


<>!£•  Floors. 

6th.  Ft.  Spat* 

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TYPICAL  FLOOR   FRAMING   PLAN-. 

f  /A!  -  /*  ry.  «_  /w/?i 

\lSlVK~ATH.FLndtt     SIMILAR. 

/7 

Plate.  F.     Typical  Floor  Framing  Plan,  Fifth  to  Sixteenth  Floors  Inclusive.  Fort  Dearborn 

Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


r 

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Plate 


G.     Roof  Framing  Plan,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


A  0/?S£3 

Plate  H.    .Details  of  Chimney,  Columns,  and  Bases,  Fort  Dearborn  Hote) 
Courtesy,  Holabird  &  Roche,  Architects 


TYPICAL    conn.  OF~  INTERIOR 

TO    COLUMNS 
BELOW  /OLZ  FLO  OK 


" 

/57  J6  TYPI(:AL    CQHH   Qf  INTERIOR- 


GltDCRS    TO   COLUMN*       CONN    OF  PlAGOHAL    BRACING. 
ATTiC  TO  /OL«  TLOOfS         TO    COL    J6  -37-41  14Z  AT  fil 
JiS  I.  S  12  FLOORS 


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J//VMF  LAC££> 
JECT/OH  OF 


9TH  FLOOR 


6 BAM  OF  BRACING  /kT/POJJ    SOUTH  FfiD. 

M/SCCL  L  ANZOUS     DETAILS. 

Plate  I.     Miscellaneous  Details,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  <k  Roche,  Architect* 


TYPICAL    5P/JNPREL    PET  AIL  5. 

Plate  L.     Typical  Spandrel  Details,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  <fc  floc/ie.  Architects 


Plat«  M .     Basement  and  Sub-Basement  Plans,  Fort  Dearborn  Hotel 
Cvurtcw,  Uolabird  &  Roche.  Architect* 


loo'-J." 


r/BfT    n<3JB    Pi  AM 

Plate  N.     First  Floor  Plan,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


PEA  C TiOH  ^O 7  OOO  FOR 
EACH  Gl*OC*. 


PLATE  GIRD  Eft  *T  a*  FLO  OK 


Plate  O.     Details  of  Special  Plate  Girder  at  Fourth  Floor  Showing  Offset  of  Column  33,  Fort 

Dearborn  Hotel 
Courtesy,  Holabird  A  Roche,  Architects 

*' '*' 


ft  OCR  PL  » 

Plate  P.     Second  Floor  Plan,  Fort  Dearborn  Hotel 
Courtesy.  Holabird  *  Roche.  Architect* 


"E"      E: 

±"     I      I    :i±-  I      L.^ 


Plate  Q.     Third  Floor  Plan,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


Plate  R.     Typical  Floor  Plan,  Fifth  to  Fourteenth  Floors,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


Plate  S.     Roof  Plan,  Including  Vertical  and  Horizonta  ISectiona  of  Penthouse,  Fort  Dearborn 

Hotel 
Courtesy,  Holabird  &  Roche,  Architec 


Plate  T.     Sections  of  Typical  Spandrels,  Fort  Dearborn  Hotel 
Courtesy,  Uoiabird  ifc  Ruche,  Architects 


U  LJ  U 

njg^  n 

nnn  n  n  n  n 


ngn  n  n  n  n 


Plate  U.     LaSalle  Street  Front  Elevation,  Fort  Dearborn  Hotel 
Courtesy^  Uolabird  &  Roche,  Architects 


Plate  V.     Alley  Elevation,  Fort  Dearborn  Hotel 
Courtesy;  Ilolabird  &  Roche,  Architect* 


Plate  W.     Section  of  Building  Looking  North,  Fort  Dearborn  Hotel 
Courtesy,  Holabird  &  Roche,  Architects 


'•  J-OOKMf  \/£ff- 
Plate  X.    Section  of  Building  Looking  West,  Fort  Dearborn  Hotel 
Courtesy,  Holdbird  <fc  Roche,  Architects 


294  STEEL  CONSTRUCTION 

FIREPROOFING 

Choice  of  Concrete.  The  general  subject  of  fireproofing  is  dis- 
cussed elsewhere  in  this  book.  For  this  building  concrete  is  used  for 
fireproofing  the  steel.  It  is  selected  because  it  protects  the  steel  from 
corrosion,  adds  to  the  strength  of  the  columns,  and  can  be  placed 
easily,  in  connection  with  the  concrete  used  in  the  floor  construction. 

Thickness  Required.  Tlie  fireproofing  affects  the  steel  design 
through  the  weight  of  the  material  'to  be  supported,  and  "through 
the  locations  of  steel  members  in  relation  to  the  openings,  as  allow- 
ance must  be  made  for  the  thickness  of  fireproofing.  The  thick- 
•  nesses  required  are* 

For  exterior  columns  4 

For  interior  columns  3" 

On  the  bottom  and  sides  of  beams  2" 

On  the  outside  of  spandrels  4" 
Beyond  the  edge  of  shelf  angles 
and  plates  supporting  outside 

brickwork  2" 

For  the  last  two  items,  the  brick  covering  is  the  fireproofing,  but  For 
the  columns  the  brick,  covering  is  not  counted  as  fireproofing. 

Effect  on  Position  of  Exterior  Columns,  Etc.  The  requirements 
for  thickness  of  fireproofing  control  the  position  of  exterior  columns, 
spandrel  beams,  and  beams  around  openings  in  floors.  For  example, 
assuming  that  the  steel  columns  will  be  14  inches  square,  the  smallest 
distance  that  -can  be  used  from  face  of  building  to  center  of  columns 
is  made  up  of 

One  course  of  brick  4" 

Concrete  fireproofing  4" 

One-half  of  column  width        7" 
Total  To^' 

This  value  is  adopted  for  the  columns  along  the  alley  and  court 
walls,  but  along  the  street  fronts  a  greater  distance  must  be  had  to 
suit  the  architectural  designs,  1  foot  10  inches  being  used.  The 
columns  should  be  placed  as  close  to  the  outside  of  the  building  as 
possible,  to  keep  the  eccentricity  small  and  also  to  make  the  pro- 
jection of  the  columns  into  the  rooms  as  small  as  practicable. 

In  general,  the  spandrel  girders  are  placed  as  near  the  outer 
face  of  the  wall  as  the  fireproofing  requirements  will  permit,  that  is, 

*  To  comply  with  the  Chicago  Building  Ordinance. 


STEEL  CONSTRUCTION  295 

with  the  edge  of  the  flange  2  inches  from  the  face  of  the  wall.  In 
order  to  provide  support  farther  out,  shelf  angles  or  plates  are  used, 
projecting  no  nearer  to  the  face  of  the  wall  than  2  inches.  The 
outer  2  inches  of  the  flange  angles  of  a  girder  may  be  considered  as 
shelf  angles,  if  the  area  of  this  portion  of  the  angles  is  not  required  for 
the  girder  section;  and  in  such  a  case  the  girder  is  placed  2  inches 
nearer  the  face  of  the  building  than  otherwise  would  be  done. 

Fireproofing  Around  Openings.  Around  openings,  the  speci- 
fications require  2  inches  for  fireproofing  and  usually  1  inch  is 
needed  for  plaster,  stair  facia,  or  other  finish.  To  these  must  be 
added  the  half  width  of  beam  to  get  the  distance  from  finished  edge 
of  opening  to  center  of  beam.  The  actual  amount  required  varies  for 
different  sizes  of  beams.  It  is  usually  convenient  to  use  the  next 
larger  whole  number  of  inches.  In  most  cases  6  inches  will  suffice 
for  the  distance  from  center  of  beam  to  finished  opening. 

LOADS 

Classification  of  Loads.  The  structural  frame  of  the  building 
must  support  the  weight  of  all  materials  of  construction,  called  the 
"dead  loads";  and  the  loads  of  all  kinds  that  may  be  imposed  on  the 
finished  structure,  called  the  "live  loads".  Dead  loads  are,  in  all 
cases,  gravity  loads,  that  is,  they  act  vertically.  Live  loads  are 
gravity  loads  in  most  cases.  (Belt-driven  machinery  may  cause 
loads  in  lateral  directions.)  In  addition  to  the  gravity  loads,  the 
framework  must  resist -wind  pressure. 

A  design  cannot  be  more  accurate  than  the  loads  upon  which 
it  is  based.  It  is,  therefore,  of  first  importance  that  the  loads  used 
be  as  accurate  as  practicable. 

Dead  Loads.  The  so-called  dead  loads,  that  is,  fixed  or  immov- 
able loads,  consist  of  the  weight  of  all  the  materials  of  construction. 
The  quantities  must  be  estimated  from  the  architectural  plans  and 
the  structural  plans  as  they  develop. 

Unit  Weights.  The  unit  weights  of  some  materials  will  vary 
according  to  locality  and  the  weights  of  some  will  vary  because  of  a 
difference  in  quality.  The  following  values  may  be  used  as  aver- 
ages for  ordinary  conditions.  Weights  which  are  likely  to  vary 
with  quality,  location,  or  any  other  cause  should  be  verified  or 
corrected  by  the  designer. 


296  STEEL  CONSTRUCTION 

WEIGHTS  OF  MATERIALS  OF  CONSTRUCTION 

White  pine,  spruce,  hemlock,  per  ft.,  board  measure  3  Ib. 

Yellow  pine,  fir,  per  ft.,  board  measure  4  Ib. 

Oaks,  maple,  per  ft.,  board  measure  5  Ib. 

Brick  masonry,  pressed  or  paving,  per  cu.  ft.  140  Ib. 

Brick  masonry,  hard  common,  per  cu.  ft.  120  Ib. 

Brick  masonry,  hollow,  per  cu.  ft.  90  Ib. 

Sandstone  or  limestone  rubble,  per  cu.  ft.  140  Ib. 

Sandstone  or  limestone  cut  facing,  per  cu.  ft.  150  Ib. 

Granite,  per  cu.  ft.  160  Ib. 

Stone  concrete,  per  cu.  ft.  144  Ib. 

Cinder  concrete,  per  cu.  ft.  96  Ib. 

Cinder  fill  (without  sand  and  cement)  per  cu.  ft.  72  Ib. 

Mortar  and  plaster,  per  cu.  ft.  120  Ib. 
Ornamental  terra  cotta,  backed  and  filled  with  common 

brick,  per  cu.  ft.  120  Ib. 

Marble,  per  cu.  ft.  175  Ib. 

Floors,  marble,  tutti  colori,  and  similar,  per  sq.  ft.  12  Ib. 

Windows  (glass,  frames,  and  sash),  per  sq.  ft.  5  Ib. 

Roofing,  composition,  per  sq.  ft.  5  Ib. 

Roofing,  gravel,  per  sq.  ft.  10  Ib. 

Roofing,  slate,  per  sq.  ft.  10  Ib. 

Roofing,  tile,"per  sq.  ft.  10  Ib. 

Roofing,  shingle,  per  sq.  ft.  3  Ib. 

Sheet  metal  roofing,  cornice,  etc,  per  sq.  ft.  3  Ib. 

Partition  tile,  3  in.  thick,  per  sq.  ft.  14  Ib. 

Partition  tile,  4  in.  thick,  per  sq.  ft.  15  Ib. 

Partition  tile,  6  in.  thick,  per  sq.  ft.  22  Ib. 

Partition  tile,  8  in.  thick,  per  sq.  ft.  28  Ib. 

Partition  tile,  10  in.  thick,  per  sq.  ft.  32  Ib. 

Floor  flat  arch  (average  of  set)  8  in.  thick,  per  sq.  ft.  28  Ib. 

Floor  flat  arch  (average  of  set)  10  in.  thick,  per  sq.  ft.  32  Ib. 

Floor  flat  arch  (average  of  set)  12  in.  thick,  per  sq.  ft.  36  Ib. 

Floor  flat  arch  (average  of  set)  14  in.  thick,  per  sq.  ft.  40  Ib. 

Floor  flat  arch  (average  of  set)  16  in^ thick,  per  sq.  ft.  46  Ib. 
Floor  segmental  arch  tile  (average  per  set)  6  in.  thick 

at  crown,  per  sq.  ft.  28  Ib. 


STEEL  CONSTRUCTION  297 

Mortar  for  tile  arch  floors,  per  sq.  ft.  3  Ib. 

Book  tile  2  in.  thick,  per  sq.  ft.  12  Ib. 

Book  tile,  3  in.  thick,  per  sq.  ft.  14  Ib. 
Beam  tile  (when  not  included  with  arch  tile),  per  sq.  ft.     12  Ib. 

Gypsum  partition  blocks,  3  in.  thick,  per  sq.  ft.  10  Ib. 

Gypsum  partition  blocks,  4  in.  thick,  per  sq.  ft.  12  Ib. 

Gypsum  partition  blocks,  5  in.  thick,  per  sq.  ft.  14  Ib. 

Gypsum  partition  blocks,  6  in.  thick,  per  sq.  ft.  16  Ib. 

Plaster  on  brick,  concrete,  tile,  or  gypsum,  per  sq.  ft.  5  Ib. 

Plaster  on  lath,  per  sq.  ft.  7  Ib. 

Suspended  ceiling  complete,  per  sq.  ft.  10  Ib. 

Steel  bar  1  in.  square,  1  ft.  long,  per  lineal  ft.  3.4  Ib. 

Steel  plate  1  ft.  square,  1  in.  thick,  per  sq.  ft.  40.8  Ib. 

Cast  iron,  bar  1  in.  square,  1  ft.  long,  per  lineal  ft.  3. 125  Ib. 

Cast  iron,  per  cu.  in.  .26  Ib. 

The  following  items  may  vary  considerably  in  weight  but  the 
values  given  may  be  used  for  preliminary  computations,  or  when 
the  quantities  are  small : 

Iron  stair  construction,  per  sq.  ft.  50  Ib. 

Concrete  stair  construction,  per  sq.  ft.  150  Ib. 

Wood  stair  construction,  per  sq.  ft.  20  Ib. 

Sidewalk  lights  in  concrete,  per  sq.  ft.  30  Ib. 

Reinforcment  of  concrete,  per  cu.  ft.  6  Ib. 

Total  weight  of  reinforced  concrete,  per  cu.  ft.  150  Ib. 

Steel  joists,  per  sq.  ft.  of  floor  6  Ib. 

Steel  girders,  per  sq.  ft.  of  floor  4  Ib. 

Partition,  tile  plastered,  per  sq.  ft.  25  Ib. 

Same  in  hotels,  per  sq.  ft.  of  floor  35  Ib. 

Same  in  office  buildings,  per  sq.  ft.  of  floor  25  Ib. 

Live  Loads.  Live  loads  are  the  temporary  or  movable  loads 
in  a  building'.  They  include  furniture,  merchandise,  and  people. 
The  amount  of  live  load  depends  on  the  purpose  for  which  the 
building  is  used,  and  for  a  given  purpose  may  vary  greatly  from 
time  to  time  and  from  one  part  of  the  building  to  another.  The 
amount  to.be  used  is  a  matter  of  judgment,  unless  an  arbitrary 
weight  is  established  by  law.  In  most  cities  the  building  ordi- 


298  STEEL  CONSTRUCTION 

nances  fix  the  minimum  live  loads  for  various  buildings  according  to 
their  use.  The  requirements  of  the  Revised  Building  Ordinances  of 
the  City  of  Chicago,  adopted  December  8, 1910,  are  as  follows: 

Stores,  light  manufacturing,  stables,  and  garages  100  Ib. 

Office  buildings,  hotels,  and  hospitals  50  Ib. 

Dwellings,  small  stables,  and  private  garages  40  Ib. 

Churches  and  halls  100  Ib. 

Theaters  100  Ib. 

Apartment  houses  40  Ib. 

Department  stores  100  Ib. 

Schools  75  Ib. 

Roofs  25  Ib. 


These  loads  are  to  be  applied  per  square  foot  to  the  actual  fleor  area 
of  the  building. 

In  designing  the  floor  slabs  and  joists,  the  full  amount  of  the  live 
load  is  used.  For  girders,  the  live  load  may  be  reduced  15  per  cent. 
For  columns,  the  load  for  the  top  floor  is  reduced  15  per  cent  and 
for  each  successive  floor  downward  the  reduction  is  increased  5  per 
cent  till  50  per  cent  is  reached;  this  final  value  is  used  for  the  remain- 
ing floors.  This  method  of  reducing  the  loads  on  columns  is  allowed 
in  Chicago.  Other  similar  methods  are  used  in  other  cities.  The 
designer  must  use  his  judgment  as  to  the  propriety  of  making  the 
reductions. 

Special  Loads.  In  addition  to  the  live  load,  which  is  assumed 
to  be  uniformly  distributed  over  the  floor,  there. may  be  special 
loads,  such  as  elevators,  machinery,  water  in  tanks,  coal  in  bins, 
space  for  storage  of  special  materials,  etc.  The  weight  of  water  is 
62.5  pounds  per  cubic  feet,  or  8J  pounds  per  gallon;  of  bituminous 
coal,  50  pounds  per  cubic  feet;  of  anthracite  coal,  60  pounds  per 
cubic  feet.  * 

The  weights  of  elevators  are  usually  given  by  the  manufacturer 
for  the  particular  situation.  An  impact  allowance  of  100  per  cent 
is  applied  to  these  weights  in  designing  the  beams  and  their  connec- 
tions to  the  columns,  but  only  the  actual  weights  need  be  allowed 
on  the  columns. 

Loads  on  the  Building  Illustrated.  In  the  Fort  Dearborn  Hotel 
the  following  live  loads  are  used : 


300 


STEEL  CONSTRUCTION 


For  the  roof,  per  sq.  ft.  25  Ib. 

For  2nd  to  16th  floor,  per  sq.  ft.  50  Ib. 

For  1st  floor,  per  sq.  ft.  100  Ib. 

For  sidewalks,  per  sq.  ft.  150  Ib. 
For  freight  receiving  room,  per  sq.  ft.        150  Ib. 

For  stairs,  per  sq.  ft.  100  "Ib. 

The  special  loads  are  the  elevator  loads  as  indicated  in  Figs. 


LOAD  AT  A  *  13.4  O0 
•  B  -  II. SCO 
••  C  -  4.90O 
-  U"  Z./OO 


SUPPORTS  MARKED  X-X  TO 
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STRUCTURAL     STEEL. 

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£L£VATOf?  CO.    ..     •• 

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FREIGHT  ELEVATO*   MACHIHS. 
Fig.  198.     Details  of  Freight  Elevator  Machine  and  Supports 

197  and  198  and  water-tank  loads  shown  on  the  plans  of  the  pent- 
house, Plate  S. 

The  dead  loads  are  computed  in  connection  with  the  various 
members  supporting  them,  from  the  unit  values  previously  given. 


STEEL  CONSTRUCTION 


301 


The  wind  load  is  taken  at  20  pounds  per  square  foot  of  the 
exposed  area  of  the  building. 

TYPE  OF  FLOOR  CONSTRUCTION 

Two  types  of  floor  construction  are  suitable  for  this  building; 
the   flat  tile   arch  between  steel    I-beam  joists,  Fig.  199,  and  a 


OtfflteCV — i — 4\L//jL.  -41-. 


Fig.  199.     Section  of  Flat  Tile  Arch  Floor 

combination  tile  and  reinforced  concrete  spanning  from  girder  to 
girder,  Fig.  200,  and  Plates  J  and  K.  Other  types  might  be  consid- 
ered but  have  been  rejected  as  not  being  suitable  for  the  particular 
requirements  of  this  building.  It  is  evident  at  once  that  the  type 
using  joists  requires  more  steel  than  the  other,  but  in  order  to  make 
a  complete  comparison  of  costs  it  is  necessary  to  make  preliminary 
designs  of  the  steel  required  for  typical  panels  for  each  type. 


CONCRETE 


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Fig.  200.     Section  of  Reinforced  Concrete  and  Tile  Floor 

Tile  Arch  Floor.    Considering  first  the  flat  tile  arch,  the  loads 
per  square  foot  of  floor  on  joists  are 

Tile  arch  set  in  place  14  in.  deep  43  Ib. 

Concrete  3J  in.  deep  42  Ib. 

Steel  joists  6  Ib. 

Plaster  5  Ib. 

Partitions  35  Ib. 


Total  dead  load 


Live  load 


Total  load  on  joists 


131  Ib. 
_501b. 

181  Ib. 


302 


STEEL  CONSTRUCTION 


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Fig.  201.     Diagram  Showing  Framing  for  Tile  Arch  Floor 


STEEL  CONSTRUCTION  303 

The  loads  per  square  foot  of  floor,  as  applied  to  the  girder  are 

Total  dead  load  of  floor  as  above  131  Ib. 

Steel  girder  4  Ib. 

Fireproofing  on  girder  2  Ib. 

Total  dead  load  137  Ib. 

Live  load  85%  of  50  Ib.  43  Ib. 

Total  load  on  girders  180  Ib. 

Therefore,  180  pounds  per  square  feet  may  be  used  for  both  joists 
and  girders. 

The  allowance  for  partitions  is  determined  by  computing  the 
total  quantity  and  weight  on  one  floor  and  dividing  by  the  number 
of  square  feet  of  floor  area. 

The  depth  of  the  joists  is  assumed  for  trial  to  be  12  inches. 
The  joists  may  be  spaced  as  far  apart  as  8  feet,  but  a  closer  spacing 
is  preferred.  They  may  be  arranged  in  the  three  ways  shown  in 
Fig.  201. 

The  beams  15-22  and  17-24  support  the  wall  load  as  well  as  the 
floor  load.  The  amount  of  the  wall  load  is  calculated  as  follows: 

Gross  wall  area  1 1'-O"  X  19'-4"        212  sq.  ft. 
Less  windows  2X6'-4"X4'-0"  51  sq.  ft. 

Net  wall  area  161  sq.  ft. 

Weight  of  material  composing  wall  is 

4  -inch  pressed  brick  weighing  140  Ib.,  per  cu.  ft.  47  Ib. 

4-inch  common  brick  weighing  120  Ib.,  per  cu.  ft.  40  Ib. 

4J-inch  hollow  brick  weighing    90  Ib.,  per  cu.  ft.  34  Ib. 

Total  weight  per  sq.  ft.  of  wall  area  121  Ib. 

Using  even  figures,  the  weight  of  wall  on  the  spandrel  beam  is 

160  X 120  =  19,200  # 

Scheme  a.  In  scheme  a,  Fig.  201,  the  sizes  of  beams  required 
to  support  the  loads  computed  above  are  as  marked  on  the  diagram. 
The  lengths  used  in  computing  are  the  actual  lengths  of  the  beams, 
that  is,  allowance  is  made  for  the  width  of  column.  Thus  the  joist 
between  columns  16  and  23  is  taken  at  18'-2"  long,  and  because  it  is 
shorter  than  the  other  joists  it  is  made  lighter. 

Scheme  b.  Scheme  6,  Fig.  201,  is  similar  to  scheme  a,  the  only 
difference  being  in  the  spacing  and,  consequently,  in  the  weight  of 
the  joists.  It  has  the  advantage  of  using  joists  all  alike  and  equally 


304  STEEL  CONSTRUCTION 

spaced.  It  has -the  disadvantages  of  greater  weight  (slight),  greater 
number  of  pieces  to  be  handled,  and  of  not  providing  a  direct  brace 
between  columns  16-23, 

Scheme  c.  In  scheme  c,  Fig.  201,  the  direction  of  the  joists 
differs  from  that  in  the  other  schemes.  It  has  the  disadvantages  of 
a  greater  variety  of  sizes  of  joists  and  of  throwing  a  heavy  load  on 
the  spandrel  girders  which  have  eccentric  connections  to  the  columns. 
Its  advantage  (which  is  not  apparent  from  the  sketches  but  is  shown 
on  the  architectural  plans  of  the  building)  is  that  the  girders  do  not 
cross  the  corridor  which  extends  along  the  middle  of  the  building 
alongside  of  columns  16-23. 

The  weights  of  the  steel  in  the  three  schemes  differ  so  little  that 
this  feature  would  not  govern.  Scheme  a  seems  to  be  the  best  one 
because  it  has  the  least  number  of  pieces  to  handle,  braces  all  col- 
umns in  both  directions,  and  loads  the  columns  with  the  least  eccen- 
tricity. 

PROBLEMS 

1.  Estimate  the  weights  of  steel  in  the  panels  shown  in  Fig.  201  for  schemes 
a,  6,  and  c. 

2.  Check  the  sizes  of  I-beams  used  in  schemes  a,  b,  and  c. 

Combination  Tile  and  Concrete  Floor.  Now  consider  the 
type  of  floor  construction  shown  in  Fig.  200,  that  is,  the  combina- 
tion tile  and  concrete.  There  being  no  steel  joists,  the  weight  per 
square  foot  as  applied  to  the  girders  is  estimated  as  follows: 

Concrete  slab  3J  in.  42  Ib. 
Concrete  joists  4"  X 10",  40  #  X  f  30  Ib. 

TilelO"Xl2";32#Xi  24  Ib. 

Plaster  5  Ib. 

Reinforcing  steel  3  Ib. 

Girder  steel  4  Ib. 

Girder  fireproofing  10  Ib. 

Partitions  35  Ib. 

Total  dead  load  153  Ib. 

Live  load,  85%  of  50  Ib.  _43  Ib. 

Total  load  196  Ib. 

On  the  narrow  panels  the  tile  fillers  are  8  inches  deep,  the  resulting 
saving  in  weight  of  tile  and  concrete  and  concrete  joists  being  9 
pounds.  This  leaves  a  total  weight  of  187  pounds  per  square  foot 
on  these  narrow  panels. 


STEEL  CONSTRUCTION  30r> 

Two  schemes  For  the  arrangement  of  girders  are  shown  in  Fig. 
202.  In  both  cases  the  spandrel  beams  have  the  same  wall  load  as 
computed  in  connection  with  the  tile  arch  type  of  floor,  viz,  19,200 
pounds.  The  sizes  of  beams  required  are  marked  on  the  diagrams. 
Note  that  in  scheme  a  the  lighter  load  applies  in  the  narrow  panel, 
whereas  in  scheme  b  the  heavier  load  must  be  used  in  both  panels. 


fr 


r 


Fig.  202.     Diagram  Showing  Framing  for  Combination  Tile  and  Concrete  Floor 

The  members  marked  S  are  struts  which  support  only  narrow 
strips  of  floor  load  but  are  required  to  brace  the  columns  in  the 
direction  in  which  girders  do  not  occur.  For  this  purpose  light 
I-beams  or  H-sections  are  commonly  used,  but  in  this  case  reinforced 
concrete  is  used. 

Neither  scheme  has  any  definite  advantage  in  weight  of  steel. 
Scheme  a  is  adopted  because  the  arrangement  is  better  suited  to  the 
plan  of  the  floor.  The  girder  16-23  is  alongside  the  corridor  and  is 
covered  by  the  partition.  No  girder  crosses  the  corridor.  The  use 
of  the  larger  spandrel  beams  assists  in  bracing  the  building.  A 


306  STEEL  CONSTRUCTION 

definite  disadvantage  is  that  the  spandrel  beams,  carrying  large 
loads,  have  eccentric  connections  to  the  columns. 

PROBLEM 

Check  the  sizes  of  beams  given  in  Fig.  202. 

Selection  of  Floor  Type.  The  selection  of  the  type  of  floor  con- 
struction is  affected  by  a  number  of  items  in  addition  to  the  cost  of 
the  steel,  which  cannot  be  considered  in  detail  here.  Some  of  them 
are:  the  effect  of  difference  in  weight  on  the  cost  of  the  columns; 
the  effect  of  the  difference  in  weight  on  the  cost  of  foundations;  the 
relative  cost  of  the  floors;  the  thickness  of  the  floor  construction; 
and  soundproofness.  In  this  particular  case  the  cost  of  the  steel 
is  the  most  important  item. 

The  combination  type  is  used  for  this  building  on  account  of 
its  economy,  all  conditions  being  considered,  Plates  J  and  K. 

FRAMING  SPECIFICATIONS 

Arrangement  of  Girders.  Some  attention  has  already  been 
given  to  the  arrangement  of  the  girders  in  the  discussion  of 
typical  floor  panels,  but  this  arrangement  really  needs  to  be  con- 
sidered in  its  relation  to  the  entire  building.  Refer  to  the  archi- 
tectural and  the  framing  plans  of  the  typical  floors,  Plates  R  and  G. 

Exterior.  It  is  necessary  of  course  to  have  girders  around  the 
entire  perimeter  of  the  building  to  support  the  walls. 

Interior.  The  next  thing  to  settle  is  whether  the  interior 
girders  shall  be  parallel  to  or  perpendicular  to  the  outside  lines  of 
the  building  The  former  arrangement  is  used.  It  is  to  be  noted 
that  the  girders  and  their  covering  project  several  inches  below  the 
ceiling  line,  hence  it  is  important  to  place  them  so  that  they  interfere 
as  little  as  practicable  with  the  interior  arrangement.  In  the  plan 
adopted  the  principal  lines  of  girders  are  along  the  side  of  the  corri- 
dors and  thus  can  be  partially  or  wholly  concealed.  They  cross  the 
corridors  only  at  two  places. 

The  arrangement  used  gives  practically  a  set  of  duplicate  floor 
panels  along  the  outside  walls  of  the  building  and  another  along  the 
court  walls.  The  other  plan  would  be  nearly  as  good  in  this  respect. 
However,  columns  2  and  6  are  not  opposite  the  columns  in  the  next 
row  so  that  if  girders  perpendicular  to  the  outside  lines  were  used, 
they  would  be  connected  at  one  end  to  the  columns  mentioned  but 


STEEL  CONSTRUCTION  307 

would  require  cross  girders  to  support  the  other  ends.  Having  main 
lines  of  girders  east  and  west,  and  also  north  and  south,  is  advanta- 
geous in  bracing  the  building. 

Special  Cases.  On  the  first  floor,  Plate  C,  girders  are  required 
between  columns  17-19  on  account  of  the  length  of  span.  Along 
the  east  and  south  sides  no  wall  girders  are  required  because  the 
basement  walls  can  be  used  to  support  the  first-story  walls,  hence 
along  these  two  sides  the  girders  are  placed  perpendicular  to  the 
side  lines.  Other  interior  girders  are  placed  so  as  to  give  the  greatest 
possible  uniformity  in  the  floor  construction. 

Around  openings,  such  framing  is  used  as  may  be  needed.  No 
instruction  is  necessary  for  this,  as  the  framing  required  can  easily 
be  determined  from  the  conditions  in  each  case. 

Each  building  has  its  special  conditions  affecting  the  placing 
of  the  girders.  Flat  ceilings,  permitting  no  projecting  beams,  may 
compel  the  placing  of  girders  on  the  short  spans  and  perhaps  the 
use  of  double  girders.  The  use  of  reinforced  concrete  floors  with 
rods  in  two  directions  requires  girders  on  all  four  sides  of  the  panels. 
Pipe  shafts  in  line  with  the  columns  in  one  direction  may  require 
the  placing  of  the  girders  in  the  other  direction.'  Columns  in  rows 
in  one  direction,  only,  limit  the  girders  to  those  lines. 

Arrangement  of  Joists.  Having  established  girder  lines,  the 
joists,  if  used,  are  spaced  as  uniformly  as  practicable.  A  joist  should 
connect  to  each  column  in  order  to  brace  it,  and  the  intervening 
panels  should  be  divided  into  a  number  of  equal  spaces.  Their 
spacing  is  governed  in  most  cases  by  the  type  of  floor  construction; 
for  the  style  of  construction  adopted  no  steel  joists  are  required. 

Beam  Elevations.  The  elevations  of  beams  are  given  in  refer- 
ence to  the  elevations  of  the  floors.  The  distance  from  the  floor 
lines  to  the  top  of  the  beams  is  governed  by  the  floor  construction. 
The  items  entering  into  this  dimension  are:  the  thickness  of  flooring, 
whether  of  wood,  marble,  tutti  colori,  etc.;  the  mortar  bed  for 
setting  marble  and  similar  floors;  the  thickness  of  the  wood  nailing 
strips  for  wood  floors;  the  space  for  electrical  and  other  conduits. 

The  minimum  thickness  of  concrete  floors  over  beams  should 
be  3  inches  to  allow  space  for  conduits  and  to  prevent  cracks.  Other 
floors  require  from  3  to  6  inches,  depending  upon  conditions. 

In  flat  tile  arch  construction  the  total  thickness  is  fixed  by  the 


308  STEEL  CONSTRUCTION 

depth  of  the  typical  joist.  All  beams  deeper  than  this  will  be  placed 
flush  on  top,  and  all  beams  shallower  flush  on  the  bottom.  Thus, 
if  the  typical  joist  is  12  inches,  the  girder,  which  probably  is  deeper, 
will  be  placed  flush  with  the  top  of  the  joist  and  will  project  below 
the  ceiling  line;  other  joists  and  framing  around  openings  which 
may  be  8-,  9-,  or  10-inch  beams  will  be  placed  flush  with  bottom 
to  provide  bearing  for  the  skew  back  of  the  arch  at  the  proper  level. 

For  combination  tile  and  concrete,  and  for  concrete  floors,  all 
the  beams  will  be  placed  flush  on  top  except  such  as  may  require  a 
different  elevation  to  suit  some  special  condition. 

Spandrel  beams,  being  embedded  in  the  walls,  are  not  governed 
by  the  elevation  of  the  floor.  In  many  cases  these  beams  serve  as 
the  lintels  over  the  windows  and  their  elevations  are  fixed  accord- 
ingly. This  is  shown  in  the  spandrel  sections,  Plates  L  and  T. 

For  flat  roofs,  the  beams  may  be  set  on  slopes  parallel  to  the 
roof  surface,  or  may  be  set  level,  depending  on  whether  the  roof  or 
the  ceiling  has  the  greater  control. 

Arrangement  of  Columns.  Location.  It  is  desirable  that  the 
columns  be  arranged  in  rows  across  the  building  in  both  direc- 
tions, but  this  may  be  prevented  by  the  arrangement  of  the  rooms 
in  the  building.  The  column  spacing  is  also  affected  by  the  design 
of  the  exterior;  the  layout  determined  by  the  architectural  require- 
ments governs  in  most  cases.  Thus  in  the  problem  the  position 
of  column  18  is  fixed  by  the  light  court  wall;  of  columns  19  and  26 
by  the  space  required  for  elevators  and  stairs,  Plate  R;  of  column 
33  in  the  lower  part  of  the  building,  to  suit  the  arrangement  of  rooms 
in  the  first  story,  Plate  N,  it  being  offset  at  the  fourth  floor,  Plates  Q 
and  R,  on  account  of  the  light  court  wall.  The  spacing  of  the  col- 
umns along  the  west  facade  conforms  to  the  architectural  treatment, 
an  odd  number  of  panels  being  used  to  allow  an  entrance  at  the 
center.  The  spacing  along  the  north  fagade  is  governed  chiefly  by 
the  interior  divisions. 

Distance  from  Building  Line.  The  distances  of  the  columns 
from  the  building  lines  are  governed  by  the  fireproofing,  as  has  been 
explained.  They  are  l'-10"  along  the  north  and  west  fa9ades,  l'-3" 
along  the  alley  and  court,  and  l'-0"  along  the  south  side.  This 
latter  value  is  used  because  provision  is  made  for  a  building  on  the 
adjoining  lot  which  will  supply  any  additional  protection  needed. 


STEEL  CONSTRUCTION  309 

DESIGN  OF  STEEL  MEMBERS 

Design  of  Beams.  The  spacing  of  columns,  arrangement  of 
girders,  and  type  of  construction  being  settled,  the  next  step  is  the 
design  of  the  beams. 

Joists.  There  are  no  joists  except  in  a  few  cases  and  these  can 
better  be  classed  as  special  beams.  Joists  when  used  are  almost 
invariably  simple  beams  with  uniformly  distributed  loads.  There- 
fore, having  computed  the  total  load  per  square  foot  of  floor,  and 
having  fixed  the  span  and  spacing,  the  total  load  on  the  beam  is  the 
product  of  these  three  quantities,  and  from  it  the  size  of  beam  is 
taken  from  the  tables.  Or,  if  the  size  has  been  selected,  the  capac- 
ity for  the  given  span  can  be  taken  from  the  tables;  and  from  this 
the  floor  area  which  it  will  support,  and  then  the  maximum  spacing 
can  be  determined.  The  length  of  span  and  of  load  area  used  is  the 
distance,  center  to  center,  of  girders  if  the  joist  frames  between 
girders,  and  the  actual  length  of  the  joist  if  it  connects  to  columns. 

Girders.  The  typical  girders  were  designed  in  connection  with 
the  preliminary  study  of  the  floor  construction.  The  special  cases 
remain  to  be  designed.  For  example  take  girders  8-9  and  10-11. 

Girder  8-9  typical  floor,  Plate  F,  span  18'-6".  Load  area  on 
one  side  only. 

Total  load  u.  d.        1  8'-6*  X  1  0'-O'Xl  96  #  =  36,260  # 
This  requires  a  15"  I  42  # 

Girder  10-11  typical  floor,  span  15'-3".  Heavier  slab  north  side, 
lighter  span  south  side. 

.   /15'-3"X10'-0"X196#  = 
Total  load  u.  d. 


47,000  # 
This  requires  an  18*  I  46  #* 

On  the  first  floor  all  the  slabs  are  built  with  10-inch  tile  and 
provision  is  made  for  a  marble  or  a  tutti  colori  floor.  The  live  load 
allowance  is  1QO  pounds  per  square  foot.  The  partition  allowance 
can  be  reduced  to  20  pounds  per  square  foot  because  of  the 
larger  rooms.  Therefore,  the  load  per  square  foot  carried  by  the 
girder  is 

'Light  weight  Carnegie  beam.    These  special  beams  are  not  always  available, 


310  STEEL  CONSTRUCTION 

Marble  floor  10  Ib. 

Mortar  10  Ib. 

Concrete  slab  3£"  42  Ib. 

Concrete  joists  4"  X 10",  40  #  X  f          30  Ib. 

Tile  10" X 12",  32 #X|  24  Ib. 

Plaster  5  Ib. 

Reinforcing  steel  3  Ib. 

Girder  steel  4  Ib. 

Girder  fireproofing  10  Ib. 

Partitions  20  Ib. 

Total  dead  load  158  Ib. 

Live  load  85%  of  100  Ib.  j85  Ib. 

Total  load  243  Ib. 

Applying  this  to  girder  8-9,  which  has  a  span  18'-6",  gives 

Total  load  u.  d.        18'-6"  X  19'-5"  X  243  #  =  87,480  # 
This  requires  a  24"  I  69 J# 
PROBLEMS 

1.  Design  girder  9-10,  typical  floor;  girder  17-19,  first  floor;  and  girder 
13-20,  first  floor,  Plates  F  and  C. 

2.  Compute  the  total  load  per  square  feet  of  floor  in  the  freight  room  on 
the  first  floor  (panel  29-30-81 '-86).    Floor,  a  reinforced  concrete  slab  8  inches 
thick.    See  Plates  C  and  N  for  construction  of  floor.    No  partitions.    Live 
load  150  pounds.    Design  the  bejim  across  the  center  of  the  panel. 

3.  Compute  the  load  on  the  roof  girders,  und  design  girders  8-9,  9-10, 
and  10-11.    (See  Plates  G  and  J.) 

Spandrel  Girders.  The  spandrel  girders  in  this  design  carry  in 
most  cases  one-half  panel  of  floor  load  and  a  panel  of  wall.  The 
spandrel  girders  of  the  typical*  panels  of  the  typical  floors  were 
designed  in  the  study  of  the  floor  types. 

The  spandrel  girder  1-8,  typical  floor,  carries  only  the  wall 
load;  this  is  practically  uniformly  distributed.  The  -wall  in  this 
panel  is  17  inches  thick;  its  weight  per  square  foot  of  surface  is 
computed  thus: 

4  in.  pressed  brick,  140  Ib.,  per  cu.  ft.  47  Ib. 
8i  in.  common  brick,  120  Ib.,  per  cu.  ft.  85  Ib. 
4J  in.  hollow  brick,  90  Ib.,  per  cu.  ft.  34  Ib. 

166  Ib. 

The  wall  surface  is  the  panel  area  less  the  window  area,  viz, 
ll'-0"Xl8'-4"  201  sq.ft. 

Less  2  X  3'-6"  X  6'-0"          42  sq.  ft. 

Net  area  159  sq.  ft. 


STEEL  CONSTRUCTION  311 

Therefore  the  weight  on  the  girder  is 

166X159  =  26,400# 

The  span  is  IS'-G*.  This  requires  a  15"  I  36  #.  More  exact  compu- 
tations would  take  into  account  the  position  of  the  windows,  weight 
of .  concrete  around  beams,  and  weight  of  girder,  but  would  not 
change  the  result  in  this  case. 

The  effect  of  the  wind  stresses  on  the  spandrel  girders  is  con- 
sidered later  in  the  text. 
PBOBLEMS 

1.  Design  spandrel  girder    1-2,    typical  floor. 

2.  Design  spandrel  girder  10-17,  typical  floor. 

3.  Design  spandrel  girder  18-17,  typical  floor. 

Special  Beams.  Special  beams  are  required  around  elevators 
and  stairs,  and  for  the  support  of  elevator  machinery,  chimney, 
penthouses,  and  tanks. 

Panel  80-31-88-37.  The  panel1  80-31-38-87  contains  several 
special  features,  viz,  a  stairway,  an  elevator  shaft,  a  chimney  and 
vent  space,  and  a  pipe  shaft.  There  is  only  a  small  section  of  floor 
in  the  panel,  adjacent  to  column  37  on  the  typical  floor. 

In  the  north  half  of  the  panel  the  8-inch  I -beams  support  only 
partitions.  None  of  them  are  fully  loaded,  but  this  size  is  considered 
the  minimum  for  this  situation. 

The  stair  load  may  be  taken  at  50  pounds  per  square  foot  for 
the  dead  load  and  100  pounds  per  square  foot  for  the  live  load. 
It  is  supported  by  the  8-inch  I-beam  near  column  37,  and  the  span- 
drel beam  81-38.  The  latter  beam  cannot  be  placed  at  the  floor 
level  because  the  windows  just  above  the  stair  landing  interfere,  so 
it  must  be  placed  near  the  level  of  the  stair  landing. 

Framing  around  stairwells  should  be  so  designed  that  the  weight 
of  the  stair  can  be  supported  from  either  the  sides  or  the  ends.  In  some 
cases  the  entire  stair  load  is  carried  by  the  stringers  to  the  beams  at 
the  ends  of  the  well  and  in  other  cases  hangers  and  struts  transmit 
the  loads  to  the  side  beams.  Usually  this  cannot  be  determined 
by  the  structural  steel  designer  unless  he  designs  the  stair. 
PROBLEM 

Design  the  cross  beam  near  the  middle  of  panel  30-31-38-37,  typical  floor. 

Panel  19-20-27-26.  The  special  framing  in  the  panel  19-20- 
27-26,  Fig.  197  and  Plate  F,  provides  for  elevators  and  stair.  It 
presents  no  unusual  features. 


312 


STEEL  CONSTRUCTION 


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Floor  Live  Load  
Floor  Dead  Load.  .  . 
Wall  Load,  8-1  
Wall  Load,  8-15.... 
Column  and  Coverin 

|  Total  for  Story  

Accumulated  Total. 

1  Eccentric  Effect  

1 

Column  Section.  .  .  . 

STEEL  CONSTRUCTION  313 

Penthouse.  The  penthouse,  Plates  G  and  S,  between  columns 
29-31-38-36  contains  a  number  of  special  items.  Beams  are  re- 
quired at  the  roof  level  to  support  the  penthouse  walls.  At  the  roof 
level  near  columns  29-36,  two  18-inch  I-beams  are  provided  for  the 
purpose  of  carrying  two  water  tanks  and  the  concrete  platform  on 
which  they  rest. 

The  machine  platform,  Plate  S,  at  an  elevation  of  about  18  feet 
above  the  attic  floor,  supports  the  freight  elevator  and  its  machinery. 
The  arrangement  of  the  sheave  beams  and  the  machinery,  and  the 
loads  are  given  in  Fig.  198.  As  previously  directed,  these  loads 
must  be  doubled  for  the  beams  and  their  connections.  It  is  not 
worth  while  to  figure  closely  on  the  elevator  supports.  Only  a 
small  amount  of  material  is  involved,  so  all  the  computations  should 
be  on  the  safe  side. 

With  the  liberal  treatment  of  the  elevator  loads  suggested 
above  there  remains  nothing  complicated  in  the  designing  of  the 
penthouse  framings,  but  the  work  is  tedious  on  account  of  the 
variety  of  loads  and  the  irregular  spacings. 

PROBLEM 

Check  the  framing  in  the  penthouse  between  columns  29-31-88-36,  Plates 
G  and  S. 

Sidewalk  Construction.  The  sidewalk  framing  is  shown  on  the 
first  floor  plan  of  the  building,  Plate  C.  A  strip  of  prismatic  lights 
extends  along  the  building  line,  Plate  K. 

PROBLEM 

Check  the  sizes  of  beams  used  in  the  sidewalk. 

Design  of  Columns.  Columns  8  and  9  are  selected  as  typical 
exterior  and  interior  columns  for  illustrating  the  computation  of 
loads  and  the  design. 

Loads  on  Column  8.    Fig.  203  gives  the  schedule  of  loads  on 
column  8.    The  floor  area  tributary  to  the  column  is  19'-5*fX9'-10'f, 
or  191  square  feet;  for  convenience  use  190  square  feet.    This  area 
applies  at  all  floors  and  the  roof. 
The  dead  loads  are 

Roof,  per  sq.  ft.  90  Ib. 

3rd  to  attic  floors,  per  sq.  ft.        153  Ib. 
2nd  floor,  per  sq.  ft.  170  Ib. 

1st  floor,  per  sq.  ft.  158  Ib. 


314  STEEL  CONSTRUCTION 

The  live  loads  per  square  foot  for  the  successive  floors  after 
making  the  reductions  described  on  p.  298  are, 

Roof  25    Ib.  9th  floor  25  Ib. 

Attic  floor  421  Ib.  8th  floor  25  Ib. 

16th  floor  40    Ib.  7th  floor  25  Ib. 

15th  floor  371  Ib.  6th  floor  25  Ib. 

14th  floor  35    Ib.  5th  floor  25  Ib. 

13th  floor  321  Ib.  4th  floor  25  Ib. 

12th  floor  30    Ib,  3rd  floor  25  Ib. 

llth  floor  27J  Ib.  2nd  floor  25  Ib. 

10th  floor  25    Ib.  1st  floor  50  Ib. 

Column  8  supports  one-half  of  the  wall  between  columns  / 
and  8,  and  one-half  between  columns  8  and  15.  As  these  panels 
of  wall  are  not  the  same  thickness,  they  are  estimated  separately. 
Their  respective  weights  have  been  estimated  to  be  166  pounds  and 
121  pounds  per  square  foot  for  wall  surface. 

The  wall  area  estimated  is  the  net  area  between  columns,  the 
width  of  column  for  this  purpose  being  taken  at  22  inches,  out  to 
out,  of  concrete.  The  brick  facing  for  this  width  is  estimated 
with  the  weight  of  the  column.  Between  columns  1  and  8  in  the 
typical  story,  the  total  wall  area  is  H'Xl7'-8"  or  194  square  feet. 
From  this  is  deducted  the  window  area,  Plate  V,  2x3'-6"x6'-4" 
or  44  square  feet,  leaving  a  net  area  of  150  square  feet.  One-half 
of  this,  75  square  feet,  is  carried  by  column  8.  At  other  stories 
the  area  differs  because  of  different  story  heights  and  different 
windows.  At  the  roof  in  this  panel  are  a  terra  cotta  balustrade 
and  a  cornice,  Plate  T,  and  at  the  3rd  and  4th  floors  are  belt  courses 
of  terra  cotta  projecting  beyond  the  wall  line.  These  are  irregular 
in  shape  but  their  dimensions  can  be  scaled  and  their  approximate 
weights  computed  at  the  rate  of  120  pounds  per  cubic  foot. 

Between  columns  8  and  15  in  the  typical  story,  the  area  sup- 
ported by  column  8  is  H'Xl7'-6"  or  192  square  feet.  From  this  is 
deducted  the  window  area  2x4'x6'-4"  or  51  square  feet,  leaving 
a  net  area  of  141  square  feet.  One-half  of  this,  70  square  feet,  is 
carried  by  column  8.  Note  that  the  small  window  is  neglected. 

At  the  roof  there  is  a  parapet  wall  the  dimensions  of  which  can 
be  scaled  from  the  drawings. 


STEEL  CONSTRUCTION  315 

The  basement  and  first  story  walls  are  not  supported  by  the 
steel  framework. 

For  the  weight  of  the  column  and  covering  an  average  amount 
per  foot  ot  length  is  computed  and  used  for  the  whole  length  thus: 
Steel  150  Ib, 

Concrete  (22X22  less  40)  say       450  Ib. 
Brick  facing  4"  X22*  say  90  Ib. 

690  Ib. 
This  amount  is  too  large  at  the  top  and  too  small  at  the  bottom. 

From  the  foregoing  data  the  loads  on  column  8  are  computed 
and  entered  in  the  schedule  in  Fig.  203.  For  the  column  section  in 
any  given  story  the  loads  entered  are  the  weight  of  the  column  in 
that  story,  the  weight  of  the  floor  above,  and  the  weight  of  the  walls 
in  the  story  above. 

As  the  loads  are  entered,  the  eccentricity,  il  any,  is  noted  as 
indicated  by  the  letter  e.  At  all  floors  from  the  second  to  the 
roof,  one-half  of  the  floor  load  comes  to  the  column  through  the 
girder  8-9  and  one-half  through  8-15.  These  connect  on  opposite 
sides  and  balance  each  other.  At  the  first  floor  the  entire  floor 
load  connects  to  one  flange  and,  therefore,  is  eccentric.  The  wall 
loads  are  eccentric  throughout,  but  at  the  second  floor  the  wall  load 
1-8  is  only  slightly  so  and  is  on  the  opposite  side  of  the  axis  from 
the  wall  load  8-15.  In  the  schedule,  on  the  line  marked  "eccentric 
effect",  are  given  the  concentric  equivalents  of  the  eccentric  loads 
computed  from  the  formula 


No  serious  error  is  committed  if,  for  the  shape  of  column  here  used, 
the  value  of  r  is  taken  at  eight-tenths  of  c.  The  result  can  be  checked 
back  and  the  error  corrected,  if  necessary,  after  the  section  has  been 
selected.  The  values  in  the  schedule  are  computed  on  this  basis 
but  the  amount  entered  is  three-fourths  of  the  computed  amount. 
Thus  for  the  attic  story  column  tfre  computations  are 

JF'e=22,300X  1*^=40,600,  say  40,000# 
0X0 

Three-fourths  of  this  is  30,000,  which  amount  is  used.  At  all  the 
typical  floors,  the  result  is  so  close  to  this  amount  that  it  may  be 
used  from  the  second  story  to  the  roof. 


316 


STEEL  CONSTRUCTION 


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Floor  Dead  Load  
Column  and  Covering 

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|  Accumulated  Total.  .  . 

|  Eccentric  Effect  

1 

r1 

I  Column  Section  

STEEL  CONSTRUCTION  317 

The  eccentric  effect  at  the  first  floor  (on  basement  column)  is 
W't  =  39,500  x~^  =  62,000  #  (approx.) 


three-fourths  of  this  is  46,500  pounds. 

Note  that  the  eccentric  effect  is  not  cumulative. 
Loads  on  Column  9.  The  loads  on  column  9  are  much  simpler, 
consisting  only  of  the  weight  of  the  column  and  the  floor  loads.  The- 
floor  area  is  f  9'-5"  X  16'-6"  or  320  square  feet.  On  the  floors,  second  to 
attic,  the  part  of  this  area  in  the  panel  9-10-17-16  is  lighter  than  the 
rest  of  it.  This  is  taken  into  account  in  the  following  dead  loads: 

Roof,  per  sq.  ft.  90  Ib. 

3rd  to  attic  floors,,  per  sq.  ft.          150  Ib. 

2nd  floor,  per  sq.  ft.     '  167  Ib. 

1st  floor,  per  sq.  ft.  158  Ib. 

The  weight  of  the  column  per  lineal  foot  is 

Steel  150  Ib. 

Concrete  (20X20  less.40)  360  Ib. 

Total          510  Ib. 

At  each  floor  there  is  eccentricity  due  to  the  unequal  loads  from  the 
girders  8-9  and  9-10.  On  all  floors  from  second  to  roof  160  square 
feet  of  the  total  area  are  applied  to  the  column  through  girder  9-16 
which  connects  to  the  web  and  is  not  eccentric;  96  square  feet  are 
applied  through  girder  8-9  ';  and  64  square  feet  through  girder  9-10. 
The  difference  between  the  last  two  amounts,  32  square  feet,  is  the 
unbalanced  area  producing  eccentricity. 

The  loads  in  the  schedule  for  column  9,  Fig.  204,  are  computed 
from  the  foregoing  data. 

The  eccentric  effect  is  small  and  to  save  tedious  calculations 
can  be  computed  for  average  conditions  at  a  typical  floor  and  the 
result  applied  to  all  floors  except  the  first.  Thus,  at  the  fourteenth 
floor  the  total  of  dead  and  live  loads  is  60,000  pounds;  one-tenth  of 
this,  or  6,000  pounds,  is  unbalanced  and,  hence,  is  eccentric.  The 
values  of  e  and  c  are  equal  and  may  be  assumed  7  inches;  r  may  be 
assumed  5  inches. 

W.  =  6'00,°*,7X7  =  12,000#  (approx.) 


According  to  the  rule  adopted  three-fourths  of  this  amount  is  used, 
that  is,  9,000  pounds.  ,  This  is  applied  at  all  floors  except  the  first,' 


318  STEEL  CONSTRUCTION 

where  the  load  conditions  are  different.  After  the  column  section 
is  selected,  the  eccentric  effect  may  be  checked,  using  the  actual 
values  of  e,  c,  and  r. 

Column  Section.  Type.  The  column  section  adopted  for  this 
building  is  the  H-section  built  of  plates  and  angles.  It  is  selected 
because  of  its  ease  of  manufacture,  ease  of  making  connections  both 
to  web  and  to  flanges,  and  for  commercial  reasons. 

Location.  The  position  of  the  column  as  to  the  direction  of 
greatest  stiffness  has  been  discussed,  and  in  both  of  the  examples 
the  column  is  placed  so  that  the  stronger  way  resists  the  eccentric 
moment  of  the  load. 

Size.  It  is  desirable,  though  not  of  great  importance,  that  the 
general  size  of  the  column  be*  maintained  throughout  the  height. 
For  this  reason  a  12-inch  web  plate  is  used,  although  this  might  be 
made  10  inches  in  the  upper  stories  and  14  inches  in  the  lower  stories. 
If  column  8  were  made  10  inches  in  the  upper  stories,  the  eccentric 
effect  would  be  so  increased  that  the  section  required  would  prob- 
ably be  greater  than  for  the  12-inch  column.  The  use  of  the  14-inch 
web  plate  in  the  lower  stories  would  decrease  the  weight  of  the 
columns  but  would  make  the  finished  columns  larger  and  thus  reduce 
valuable  floor  space? 

Length.  The  columns  are  made  in  two-story  lengths,  the 
splices  in  this  case  being  made  at  the  even  numbered  floors,  that  is, 
at  2,  4,  6,  etc.  The  columns  which  extend  through  the  sub-basement 
are  made  in  three-story  lengths  to  bring  the  splice  at  the  second 
floor  so  as  to  be  at  the  same  level  as  the  others.  The  cross. section 
of  any  length  of  column  is  governed  by  the  stress  in  the  lower  of 
the  two  stories  comprising  that  length. 

Summary.,  Having  the  loads  computed  as  given  in  the  sched- 
ules and  having  established  the  foregoing  general  conditions,  it  only 
remains  to  select  from  the  tables  in  the  handbooks  the  sections 
required  for  the  several  lengths  of  column  and  enter  them  in  the 
schedule.  (See  also  Plate  H). 

In  designing  these  columns*  the  maximum  thickness  of  metal 
used  is  |  inch;  because  any  metal  thicker  than  this  would  require 
reaming  or  drilling  and  thus  add  to  the  cost.  When  the  total  thick- 

*The  tables  referred  to  on  pp.  189  and  191  were  not  used  in  making  this  design;  so  the 
identical  section  may  not  be  found  therein. 


STEEL  CONSTRUCTION  319 

ness  of  cover  plates  on  one  flange  is  more  than  f  inch,  two  or  more 
plates  are  used,  each  being  f  inch  or  less  in  thickness.     No  cover 
plates  are  used  unless  the  stress  is  beyond  the  capacity  of  a  section 
having  f-inch  metal  in  the  web  plate  and  angles. 
PROBLEMS 

1.  Compute  the  loads  and  make  the  design  for  column  16.     (Note  that 
this  column  extends  through  the  sub-basement.)     Make  schedule  as  in  Figs. 
203  and  204. 

2.  Compute  the  loads  and  make  the  design  for  column  17      (Note  that 
the  court  walls  do  not  occur  below  the  third  floor.) 

3.  Make  a  diagram  showing  the  floor  areas  supported  by  column  17  at 
the  first,  second,  third,  and  typical  floors,  Plates  C,  D,  E,  and  F. 

4.  Give  detailed  computations  of  the  wall  load  supported  by  column  17 
in  a  typical  story,  Plates  F,  R,  and  W. 

Column  Pedestals.  The  piers  under  the  columns  are  round  and, 
therefore,  in  order  to  distribute  the  load  as  evenly  as  possible,  round 
cast-iron  pedestals  of  the  type  shown  in  Fig.  152  and  Plate  H  are 
used.  The  bearing  allowed  on  the  masonry  in  this  case  is  800 
pounds  per  square  inch.  The  load  for  column  8  is  1,129,000  pounds 
and  for  column  9  is  1,132,000  pounds.  (The  eccentric  effect  is  not 
included.)  The  area  required  is  1415  square  inches,  which  corre- 
sponds to  a  circle  42  inches  in  diameter.  But  for  the  sake  of  using 
few  patterns,  the  diameter  is  made  44  inches. 

Height.  While  the  height  of  the  pedestal  is  taken  at  24  inches, 
there  is  no  very  definite  way  of  determining  the  height.  However,  a 
number  of  trial  designs  indicate  that  pedestals  of  the  type  here  used 
should  be  proportioned  as  follows: 

For  a  bearing  of  800  Ib.  per  sq.  in.,  height  53%  of  diameter 
For  a  bearing  of  600  Ib.  per  sq.  in.,  height  43%  of  diameter 
For  a  bearing  of  400  Ib.  per  sq.  in.,  height  35%  of  diameter 
Top.    The  size  of  the  top  of  the  pedestal  is  controlled  by  the 
detail  of  the  base  of  Xhe  column.     It  must  extend  far  enough  beyond 
the  hub  to  provide  holes  for  connecting  to  the  column;  2J  inches  at 
the  narrow  place  is  usually  enough  and  this  is  available  to  resist  the 
bending  moment.     The  thickness  is  assumed  arbitrarily  at  li  inches. 
Ribs.    The  number  of  ribs  assumed  is  eight.    Their  thickness 
is  not  less  than  one-twentieth  the  height,  that  is,  1J  inches. 

Diameter  of  Hub.  The  diameter  of  the  hub  is  made  such  that 
the  greater  part  of  the  column  section  is  directly  over  it.  In  this 
case  11  inches  inside  diameter  is  suitable.  The  thickness  of  the  hub 


320  STEEL  CONSTRUCTION 

must  be  such  that  its  area  together  with  that  of  the  ribs  under  the  top 
plate  will  support  the  column  load  at  10,000  pounds  per  square  inch. 
Thus  the  total  area  required  is  113  square  inches.  The  area  of  the 
ribs  to  be  counted  is  8x2i"XlJ"  or  25  square  inches,  thus  leaving 
88  square  inches  to  be  provided  in  the  hub.  This  requires  2J  inches 
thickness  of  metal,  which  makes  the  outside  diameter  15|  inches. 
The  area  of  the  11-inch  circle  is  95'square  inches,  and  of  the  15i-inch 
circle  188  square  inches;  the  difference,  93  square  inches,  is  slightly 
more  than  required. 

The  thickness  of  the  bottom  plate  must  be  assumed  for  trial; 
use  2|  inches. 

The  dimensions  of  the  rim  are  fixed  arbitrarily  1J  inches  thick 
and  5  inches  high. 

Test  for  Resistance  to  Bending.  Having  determined  or  assumed 
the  thickness  of  metal  in  the  various  parts  of  the  pedestal,  it  is  now 
necessary  to  test  the  cross  section  for  its  resistance  to  bending. 
The  procedure  is  the  same  as  that  given  on  p.  220. 

Center  of  Gravity.  To  locate  the  center  of  gravity  and  the 
neutral  axis,  take  the  following: 

Bottom  plate    area4lX2f  =112.75  M112.75X   1.375=   155.05 

Hub  area    2X192X2£  =   88.90  M  88.90X12.625  =  1122.36 

Top  plate          area    2X   HX2£  =     7.50  M     7.50X23.25   =    174.37 

Rim  area    2X  5   XU=    15.00  M  15      X  5.25   =     78.75 

224.15  1530.53 

The  distance  of  the  neutral  axis  from  the  bottom  of  the  plate  is 

1530.53      AC..    , 
-^^or  6.85  inches. 

Moment  of  Inertia.  The  moment  of  inertia  of  the  section  about 
the  neutral  axis  is 


Po,,PP,.« 

For  rim  7      JVt  XliX(5)'X2  =         31 

J-<15.0X<1.6)«  =_38 

Total  moment  of  inertia  =  11,394 


STEEL  CONSTRUCTION  321 

Resisting  Moment.    The  resisting  moment  of  the  section  is 

R  M  =  300°  Xl  1>394=  4,990,000  in.-lb. 
6 .85 

The  bending  moment  of  the  load  is 

M  =  1,132,000X44X^  =  4,980,000  in.-lb. 
Hence  the  assumed  plate  has  the  required  resistance  to  bending. 


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Fig.  205.     Diagram  Showing  Bending  Moments  Due  to  Wind  Pressure 

At  columns  86, 87, 38, 40, 41,  and  42,  the  piers  are  built  centrally 
on  the  lot  line  to  support  two  sets  of  columns.  The  bases  cannot  be 
extended  beyond  the  lot  line,  so  are  made  rectangular.  Three 


322  STEEL  CONSTRUCTION 

I-beams  are  used  for  this  purpose,  as  illustrated  in  Plate  H.     The 
method  of  designing  has  been  explained  under  bearings  for  beams. 

WIND  BRACING 

.Wind  Loads  for  Entire  Building.  The  wind  load  is  assumed 
to  be  20  pounds  per  square  foot,  all  of  which  is  to  be  resisted  by  the 
steel  frame.  Fig.  205  is  a  diagram  on  \vhich  are  marked  the  wind 
loads  for  the  successive  stories  and  the  resulting  bending  moments 
in  the  columns  and  the  girders.  The  values  given  are  for  the  entire 
building  and,  as  the  building  happens  to  be  practically  square  in 
plan,  the  diagram  applies  for  both  directions. 

At  each  of  the  upper  floor  levels,  the  load  applied  to  the  frame- 
work is  100X11X20  or  22,000  pounds.  The  first,  second,  and  third 
floors  support  different  areas,  hence  different  loads. 

Bending  Moments,  hi  Columns.  The  bending  moments  in 
the  columns  are  computed  as  follows: 

Attic  22,000  X5i  =    121,000  ft.-lb. 

16th  story          44,000  X  5|  =    242,000  ft.-lb. 

15th  story          66,000  X  5^  =    363,000  ft.-lb, 

etc.,  etc. 

1st  story  382,500X7|  =  2,773,000  ft.-lb. 

Basement         397,000  X  6  =  2,382,000  ft.-lb. 
In  Girders.    The  bending  moments  in  the  girders,  according 
to  the  rule  previously  established,  are  the  means  between  the  bending 
moments  in  the  columns.    The  values  are 

Roof  121,000+^00,000 

Attie  floor  121.000+ 


floor  242,000+    363.000  =    3^^ 

« 

etc.,  etc. 

2nd  floor          2.393.000+2.773.000,^^^  ^ 

1st  floor 


STEEL  CONSTRUCTION  323 

Note  that  the  bending  moments  in  the  girders  given  above  are 
for  one  side  only  of  the  column ;  an  equal  amount  occurs  at  the  other 
side,  making  the  total  amount  to  be  resisted  at  each  floor  twice  that 
given. 

Resistance  of  Spandrel  Girders.  Consider  now  the  wind  from 
the  North  or  from  the  South.  At  all  floors  resistance  is  offered  by 
the  spandrel  girders  between  columns  1-36  and  7-42  (except  at  first 
floor  1-36),  and  by  interior  and  court  wall  girders  in  a  north  and 
south  direction. 

In  the  upper  part  of  the  building,  the  girder  sections  which  are 
required  by  the  gravity  loads  are  sufficient  for  resisting  the  wind 
stresses.  The  first  step  is  to  determine  the  resistance  that  can  be 
developed  by  these  girders  and  then  find  at  which  floor  it  is  neces- 
sary to  use  special  construction.  The  connections  of  the  spandrel 
girders  are  shown  in  Plate  F  and  Fig.  190.  The  horizontal  shearing 
value  of  the  (field)  rivets  in  one  flange  at  50  per  cent  excess  values 
is  4 X. 44X15,000  or  26,400  pounds.  Then  the  resisting  moments  for 
one  end  of  each  beam  of  various  depths  are  as  follows : 

12-inch  beam  1   X  26,400  =  26,400  ft.-lb. 

15-inch  beam  IJx 26, 400  =  33 ,000  ft.-lb. 

18-inch  beam  ,  Ux  26, 400  =  39, 600  ft.-lb. 

20-inch  beam  1  §  X  26,400  =  44,000  ft.-lb. 

21-inch  beam  1JX26.400  =  46,200  ft.-lb. 

24-inch  beam  2  X  26, 400  =  52, 800  ft.-lb. 

This  applies  to  the  court  spandrels  as  well  as  to  the  outside  spandrels. 
Resistance  of  Interior  Girders.  The  connections  of  the  interior 
girders  are  shown  in  Plate  I  and  Fig.  191.  In  the  case  where  each 
flange  is  connected  by  six  f-inch  rivets,  the  horizontal  shear  resist- 
ance is6x  44  X  15,000  or  39,600  pounds.  Then  the  resisting  moments 
for  one  end  of  beams  of  various  depths  are  as  follows: 

12-inch  beam  1    X  39, 600  =  39,600  ft.-lb. 

15-inch  beam  Ijx  39,600  =  49,500  ft.-lb. 

18-inch  beam  HX  39, 600  =  59, 400  ft.-lb. 

20-inch  beam  1  §  X  39,600  =  66,000  ft.-lb. 

21-inch  beam  1  j  X 39, 600  =  69, 300  ft  -Ib. 

24-inch  beam  2  X  39,600  =  79,200  ft.-lb. 


324 


STEEL  CONSTRUCTION 


On  a  typical  floor  the  number  of  connections  and  their  values  are: 

4  spandrel  beams  15  inch  at  33,000  =  132,000  ft.-lb. 
18  inch  at  39,600  =  475,200  ft.-lb. 
21  inch  at  46,200  =  831,600  ft.-lb. 


12  spandrel  beams 
18  spandrel  beams 


4  interior  beams 
14  interior  beams 


18  inch  at  59,400  =  237,600  ft.-lb. 
21  inch  at  69,300  =  970,200  ft.-lb. 


1,438,800 


1,207,800 


2,646,600 

This  resistance  is  sufficient  at  the  eighth  floor  and  upward.  Above 
the  tenth  floor  the  interior  connections  may  be  reduced,  as  indicated 
on  Plate  I. 

The  interior  connections  cannot  be  increased  without  the  use 


6600*  /.OOX3J-50100 
bbOO*  .8 '5 X J j -J 6500 


5625  X    46X/$:  9000 
S(,25  X  ,2 1>  X  /  =   IS 00 


Fig.  206.     Diagram  Showing  Method  of  Computing  Resisting  Moment  of 
Girder  Connection 

of  brackets  which  would  project  through  the  fireproofing.  The 
spandrels  are  not  so  limited  and  brackets  can  be  used  to  increase 
their  resistance.  In  this  manner  the  resistance  to  wind  stresses  can 
be  provided  down  to  and  including  the  fourth  floor,  Fig.  192. 

Girder  Resistance  for  Third  Floor.    At  the  third  floor,  the  wall 
construction  is  such  as  to  make  desirable  deep  spandrel  girders 


STEEL  CONSTRUCTION  325 

between  columns  1-8  and  7-42.  These  girders  with  their  connec- 
tions are  shown  in  Plate  E.  The  total  amount  to  be  resisted  at  the 
third  floor  is  2X2,104,000  or  4,208,000  foot-pounds.  Of  this  about 
1,500,000  foot-pounds  are  resisted  by  the  interior  beams,  leaving 
2,700,000  foot-pounds  to  be  resisted  by  the  spandrel  beams.  Con- 
sider this  divided  equally  between  the  two  sides,  there  being  10 
connections  on  each  side,  so  that  each  connection  in  the  spandrels 
1-36  and  7-42  must  resist  135,000  foot-pounds.  This  requires  brackets 
of  the  type  shown  in  Fig.  192  for  the  I-beams  8-36  and  the  connec- 
tions shown  for  the  plate  girders,  Plate  E. 

The  computations  of  the  connection  of  the  plate  girders  are 
shown  in  Fig.  206;  a  is  the  rivet  spacing;  b  is  a  graphical  diagram 
giving  the  proportions  of  the  full  rivet  stress  for  the  rivets  at  various 
distances  from  the  center,  and  c  is  the  computations.  Thus  item  1 
is  2  field  rivets,  j-inch  diameter,  in  single  shear,  at  full  unit  stress, 
with  a  moment  arm  of  3|  feet;  item  3  is  2  field  rivets,  J-inch  diam- 
eter, in  single  shear,  at  0.72  of  the  full  unit  stress,  with  a  moment 
arm  of  2J  feet.  The  total  resistance  is  somewhat  larger  than 
required. 

The  girder  section  is  excessive,  the  depth  being  fixed  by  the 
spandrel  construction,  and  plates  and  angles  being  the  minimum 
sizes  suitable  for  this  situation. 

Girder  Resistance  for  Second  Floor.  At  the  second  floor  the 
interior  girders  are  arranged  differently,  so  their  resistance  must  be 
computed.  The  methods  just  given,  applied  here  give  172,000  foot- 
pounds as  the  bending  moment  at  each  spandrel  connection.  The 
connections  to  the  columns  are  designed  in  the  manner  previously 
illustrated,  Plate  D. 

Girder  Resistance  for  First  Floor.  At  the  first  floor  there  are 
no  spandrel  girders  between  columns  1-36.  The  columns  in  this 
row  are  bedded  in  the  basement  wall.  The  wall  is  assumed  to  resist 
one-half  of  the  wind  stress  at  this  floor.  The  other  half  of  the  stress 
is  resisted  by  the  interior  girders  20-41  and  the  spandrel  girders  7-4#, 
Plate  C. 

The  mistake  is  sometimes  made  of  neglecting  the  wind  bracing 
at  the  first  floor.  This  is  the  most  important  place  where  it  should 
be  given  attention.  It  cannot  be  expected  that  the  pressure  will  be 
transmitted  to  the  earth  at  a  higher  level  than  the  basement  floor. 


326  STEEL  CONSTRUCTION 

Proof  of  Column  Sections.  It  remains  to  be  determined 
whether  the  column  sections  are  overstressed  by  adding  the  wind  stress 
to  the  gravity  stresses.  One  case  serves  to  illustrate  the  method. 

At  the  second  floor,  the  bending  moments  in  column  8,  corre- 
sponding to  those  in  the  connecting  spandrel  girders,  are  160,000 
foot-pouniis  and  184,000  foot-pounds  above  and  below  the  floor, 
respectively.  Consider  the  first-story  column.  This  bending  mo- 
ment is  based  on  a  moment  arm  of  1\  feet.  The  critical  section  is 
at  the  base  of  the  bracket  which  is  3  feet  below  the  center  of  the 

41 
girder.    At  this  point  the  bending  moment  is  184,000  X^or  108,000 

foot-pounds,  or  1,296,000  inch-pounds. 
The  column  section  in  the  first  story  is 

1  web  plate  12"X  ?" 

4Ls  6"X4  "Xf 

6  cover  plates        14"  X  |" 

The  bending  is  about  the  axis  which  is  parallel  to  the  web,  so  the 
values  of  c  and  r  must  be  taken  in  reference  to  this  axis,  c  is  7  inches, 
one-half  of  the  width  of  cover  plate,  and  r  taken  from  the  tables  for 
this  column  is  3.5.  Then  the  concentric  equivalent  load  is 


The  gravity  load  on  this  column  is  1,088,000  pounds,  making 
the  total  for  which  it  must  be  designed  1,828,000  pounds.  The 
length  may  be  taken  at  11  feet  on  account  of  the  depth  of  bracket. 
According  to  the  column  formula,  this  section  is  good  for  1,196,000 
pounds.  For  the  combined  stress  this  is  increased  50  per  cent  and 
equals  1,794,000  pounds.  As  this  is  within  2  per  cent  of  the  required 
capacity,  it  is  accepted. 

The  designer  is  warranted  in  making  liberal  assumptions  as  to 
the  lengths  of  columns  and  the  allowance  of  excess  stress  when  they 
are  built  into  substantial  masonry  walls. 

This  case  illustrates  the  desirability  of  carrying  as  much  of  the 
wind  load  as  practicable  on  the  interior  columns  and  girders,  other- 
wise the  exterior  columns  may  need  to  be  increased  above  the  re- 
quirements of  the  gravity  loads  in  order  to  take  the  heavy  wind 
stresses. 


STEEL  CONSTRUCTION  327 

In  cases  like  that  above,  it  may  be  best  to  turn  the  columns  in 
the  other  direction.  It  is  simply  a  question  whether  the  effect  of 
the  wind  stress  is  more  important  than  the  effect  of  the  eccentric 
gravity  loads. 

Other  Wind  Stresses.  Now,  consider  the  wind  from  the  East 
or  from  the  West.  It  happens  that  the  south  wall  of  the  building 
is  solid,  so  that- diagonal  bracing  can  be  used,  as  shown  in  Plate  I, 
and  such  bracing  is  designed  to  take  one-half  of  the  wind  stress  in  this 
direction.  At  the  ninth  floor  a  strut  extends  across  the  court  so  that 
the  two  sets  of  bracing  co-operate  below  that  level.  The  other  half  of 
the  wind  stress  is  carried  by  the  interior  east  and  west  girders  and 
the  spandrel  girders  1-7.  The  problems  involved  do  not  differ 
from  those  that  have  been  described. 

MISCELLANEOUS  FEATURES 

Chimney  and  Its  Supports.  The  chimney,  Plates  H  and  I,  is 
located  near  column  31.  It  extends  from  the  sub-basement  floor 
to  the  top  of  the  penthouse.  It  is  made  of  steel  plates.  The  thick- 
ness of  plates  is  arbitrary,  the  chief  consideration  being  durability. 
The  chimney  is  lined  inside  with  an  insulating  material  which  is 
supported  by  shelf  angles  spaced  3  feet  apart.  The  chimney  is 
designed  to  be  built  in  sections  corresponding  to  the  two-story 
column  lengths.  The  sections  are  joined  together  by  means  of 
flange  angles  and  bolts. 

The  entire  weight  of  the  chimney  must  be  carried  from  one 
support,  as  its  length  varies  with  changes  in  temperature.  So  far 
as  the  finished  structure  is  concerned,  it  could  rest  on  the  sub-base- 
ment floor,  but  for  convenience  in  erection  it  is  supported  at  the 
first  floor.  Thus  it  can  be  erected  along  with  the  structural  steel, 
the  basement  and  sub-basement  sections  being  placed  at  any  con- 
venient time  afterward.  Usually  the  sub-basement  work  is  not 
done  until  after  the  steel  framework  is  erected  and  it  would  then  be 
difficult  to  get  the  chimney  into  place. 

The  details  of  the  breeching  connection  are  given  to  control 
both  the  structural  steel  fabricator  and  the  builder  of  the  breeching. 

Masonry  Supports.  Along  the  two  facades  at  the  first  floor 
are  some  granite  bases  which  require  supports.  These  supports, 
detailed  in  Plate  C,  are  made  independent  of  the  sidewalk  construe- 


328  STEEL  CONSTRUCTION 

tion  so  that  the  granite  can  be  set  in  advance  of  building -the  side- 
walk and  also  so  it  will  not  be  affected  by  any  possible  settlement 
of  the  sidewalk. 

At  all  floor  levels  or  other  convenient  points,  provision  must  be 
made  for  supporting  the  masonry  across  the  face  of  the  columns. 
This  can  be  done  on  this  building  in  most  cases  by  extending  a  part 
of  the  spandrel  sections  across  the  column.  But  in  many  buildings 
special  shelves  must  be  built. 

Lintels.  Most  of  the  spandrel  girders  are  so  located  that  they 
serve  as  lintels  over  the  windows.  Plates  are  riveted  on  the  bottom 
flange  over  these  openings  to  support  the  outer  course  of  bricks  or 
the  terra  cotta  lintel.  The  edge  of  the  plate  is  placed  2  inches  back 
from  the  outer  face  of  the  brickwork.  Some  designers  prefer  to 
extend  these  plates  the  entire  length  of  the  girder  to  support  the 
face  brick,  Plates  L  and  T.  When  the  windows  are  not  high  enough 
for  the  above  lintel  detail,  detached  angle  lintels  are  used. 

Spandrel  Sections.  On  burldings  having  elaborate  facades, 
many  special  details  must  be  designed  for  supporting  the  masonry* 
The  spandrel  sections  on  this  building,  Plates  L  and  T,  are  com- 
paratively simple. 

At  the  second  floor  a  projecting  plate  is  .used  along  the  bottom 
flange  of  the  girder.  At  the  third  floor  a  similar  plate  is  used  and, 
at  the  top  of  the  girder,  brackets  project  out  for  supporting  a  belt 
course  of  terra  cotta. 

Ornamental  metal  balconies  at  the  seventh,  ninth,  eleventh, 
and  thirteenth  floors  are  supported  by  light  angle  brackets  riveted 
to  the  girders. 

A  terra  cotta  balcony  at  the  fifteenth  floor  requires  the  special 
framing  shown  for  it. 

In  general,  wherever  terra  cotta  is  used,  anchor  holes  are  re- 
quired in  the  structural  steel.  It  is  the  duty  of  the  designer  to 
secure  the  necessary  data  and  put  it  on  the  drawings.  These  holes 
usually  are  spaced  about  six  inches  apart  horizontally.  Only  the 
vertical  dimensions  need  be  supplied. 

The  cornice  support  is  quite  similar  to  that  of  the  terra  cotta 
course  at  the  third  floor.  For  wide  cornices,  brackets  project  from 
the  columns,  and  these  brackets  carry  beams  for  the  support  of  the 
terra  cotta.  Every  case  requires  its  special  design. 


STEEL  CONSTRUCTION  329 

Flag  Pole  Support.  Near  column  7  on  the  roof  plan,  Plate  G, 
is  shown  a  pair  of  channels  for  supporting  a  flag  pole.  A  similar 
pair  of  channels  occurs  at  the  attic  floor.  On  some  buildings  the 
flag  pole  can  be  connected  directly  to  a  column.  This  is  the  simplest 
and  most  desirable  scheme.  In  some  cases  it  may  be  set  in  sockets 
on  the  roof  and  braced  with  angle  or  other  struts. 

No  data  are  known  to  the  writer  regarding  the  load  on  a  flag 
pole.  A  load  of  20  pounds  per  square  foot  applied  to  the  area  of  the 
flag  seems  sufficient  to  cover  the  actual  wind  pressure  and  vibration. 

Mullions.  Where  the  space  between  windows  is  not  enough  to 
permit  a  substantial  masonry  pier,  the  mullion  should  be  reinforced. 
I-beams,  tees,  or  angles  may  be  used,  depending  on  the  conditions. 
In  this  case  two  rods  are  built  into  the  brickwork,  Plate  L. 

Anchors.  The  anchor  rods  shown  extending  through  the  span- 
drel girders  and  into  the  concrete  slab  hold  the  spandrel  girders 
laterally  and  make  a  rigid  connection  between  the  framework  and  the 
floor  construction,  Plate  L. 

DIMENSIONING  DRAWINGS 

Base  Lines.  The  base  lines  for  horizontal  dimensions  are  the 
building  lines  of  the  structure.  They  are  shown  on  the  first-floor 
plan,  Plate  C.  The  building  lines  nominally  represent  the  outside 
lines  of  the  building  walls.  In  reality  they  are  often  imaginary 
reference  lines,  for,  on  account  of  the  offsets,  parts  of  the  wall  may 
extend  beyond  these  lines  and  other  parts  be  inside  of  them.  For 
the  class  of  buildings  under  consideration,  the  building  lines  usually 
coincide  with  the  lot  lines.  If  they  do  not,  then  the  lot  lines  should 
be  shown  and  dimensioned  from  the  building  lines.  If  the  corners 
of  the  building  are  not  exactly  right  angles,  the  angles  must  be 
marked  on  the  first-floor  plan.  The  cardinal  points  of  the  compass 
should  be  marked  with  approximate  accuracy  on  the  first-floor  plan. 
One  of  these  points  is  used  as  a  reference  in  marking  one  side  of 
columns  and  one  end  of  girders  for  convenience  in  erecting;  thus 
E  on  the  east  face  of  a  column,  or  N  on  the  north  end  of  a  girder. 

Column  Centers.  Having  established  the  building  lines,  the 
next  step  is  to  dimension  the  column  centers.  The  simplest  situa- 
tion is  had  when  the  building  is  rectangular  and  the  columns  are  in 
rows  in  both  directions.  Then  two  lines  of  dimensions  will  suffice 


330 


STEEL  CONSTRUCTION 


to  fix  the  location  of  all  columns,  Plate  D.    Any  irregularity  of 
spacing  in  any  row  requires  a  special  line  of  dimensions  in  that  row. 


Fig.  207.     Diagram  Showing  Method  of  Dimensioning  Column  Centers  in  an  Irregular  Building 

With  anr  irregularly  shaped  building,  the  dimensioning  becomes 
more  complicated.  One  building  line  should  be  adopted  as  a  refer- 
ence line,  taking  the  one  to  which  the  greatest  number  of  column 
lines  are  perpendicular  and  parallel.  Then  all  columns  should  be 
located  by  dimension  lines  perpendicular  and  parallel  to  this  refer- 
ence line,  that  is,  by  rectangular  co-ordinates.  The  only  diagonal 
dimensions  needed  are  those  along  which, 
or  parallel  to  which,  steel  members  are 
placed. 

In  Fig.  207,  the  reference  line  used 
is  the  south  building  line.  The  building 
lines  in  this  case  are  probably  lot  lines. 
Their  lengths  and  the  angles  are  de- 
termined by  a  survey.  The  distance 
from  the  lot  lines  to  the  column  centers 
is  established  at  I'-IO*  on  all  sides.  The 
spacing  of  columns  1  to  7  and  the  ar- 

Fig.  208.     Construction  Diagram  for      J 

Details  of  Figure  207  rangement  of  the  other  columns  are  fixed 

by  architectural  conditions. 

From  the  foregoing  data  all  the  required  dimensions  can  be 
computed  by  trigonometry.    First,  compute  the  distances  from 


STEEL  CONSTRUCTION  331 

column  7  to  the  corner  of  the  building.  From  Fig.  208  Jt  is  apparent 
that  these  distances  a  b  and  a'b  are  equal  to  each  other  and  equal  to 
caXcot  41°  15';  then 

a&  =  a'&  =  22"Xl.l40  =  25TV 
The  distance  between  columns  9  and  15  is 

20'-0"Xtan  19°  20"  =  20'-0"X.3508  =  7'-Oft" 
In  this  manner  all  the  dimensions  can  be  computed. 

PROBLEM 

Compute  the  distances  between  columns  which  are  lacking  in  Fig.  207. 

The  column  center  dimensions  should  be  repeated  on  all  the 
floor  plans.  If  the  floor  framing  plan  is  crowded,  a  separate  diagram 
at  small  scale  may  be  placed  on  the  drawing  to  display  the  column 
center  distarces. 

Girders  and  Joists.  Girders  and  joists  are  dimensioned  from 
the  column  centers.  The  dimension  lines  required  are  illustrated 
in  Figs.  201  and  202.  Note  in  Fig.  201-b  that  there  is  no  joist  at 
column  23,  so  the  space  is  divided  and  the  adjacent  joists  tied  in 
the  column.  No  dimensions  are  required  for  the  lengths  of  joists 
and  girders  other  than  those  locating  the  centers  of  the  columns 
and  beams  to  which  they  connect.  The  shop  detailer  computes 
the  actual  lengths  of  beams  required.  But  if  one  end  of  a  beam 
rests  on  a  wall,  one  face  of  the  wall  and  its  thickness  must  be  given. 

Such  details  as  struts,  mullions,  plates  for  supporting  brick- 
work, etc.,  are  also  located  from  column  centers,  as  illustrated  on 
the  floor  plans. 

Vertical  Dimensions.  The  vertical  dimensions  from  floor  to 
floor  are  given  in  a  separate  diagram  or  in  connection  with  the 
column  schedule,  Plate  H.  At  the  first  floor  a  reference  is  made  to 
established  sidewalk  grade  in  terms  of  its  elevation  above  datum, 
Plate  C.  The  elevations  of  beams  are  given  in  reference  to  the  fin- 
ished floor  elevations,  respectively.  Usually  the  elevation  of  joists 
and  girders  can  be  covered  by  a  note,  Plate  F.  Special  cases  can 
be  given  by  figures  alongside  the  beams  indicating  the  distance 
from  the  floor  level  to  the  top  flange  of  the  beam ;  thus  — 5J"  means 
that  the  top  flange  is  5|  inches  below  the  floor  line. 

Elevations  of  Spandrel  Beams.  The  elevations  of  spandrel 
beams  can  be  shown  best  on  the  sections,  where  both  the  elevation 


332  STEEL  CONSTRUCTION 

and  the  horizontal  position  can  be  given  in  relation  to  the  other 
materials  of  construction  thereabout,  Plate  L. 

Summary.  The  use  of  unnecessary  dimensions  and  needless 
repetitions  may  be  a  source  of  much  inconvenience.  It  increases 
the  probability  of  errors  and  causes  extra  work  in  checking. 

While  structural  steel  drawings  should  be  made  reasonably 
accurate  to  scale,  scaled  dimensions  must  not  be  used  in  executing 
the  work. 

The  scales  used  in  making  drawings  of  structural  steel  should 
be  as  follows:  for  framing  plans,  J  inch  or  \  inch;  for  spandrel  sec- 
tions, %  inch  or  f  inch;  and  for  details  showing  all  dimensions  and 
rivet  spacing,  1  inch  or  1 J  inches.  In  each  case  the  scale  first  given 
is  preferred.  The  use  of  a  number  of  different  scales  in  the  same 
set  of  drawings  is  objectionable. 


UNIVERSITY  CLUB  AND  MONROE  BUILDING,  CHICAGO 
Holabird  &  Roche,  Architects 


CONSTRUCTION 

PART  V 


PROTECTION  OF  STEEL 

PROTECTION  FROM  RUST 

Rust.  Although  steel  is  the  strongest  of  building  materials, 
under  unfavorable  conditions  it  may  be  one  of  th  east  durable.  Its 
great  enemy  is  rust.  The  corrosion  or  rusting  of  iron  and  steel  is 
familiar  to  every  one.  It  is  a  chemical  change  in  which  the  metallic 
iron  unites  with  oxygen  and  forms  oxide  of  iron  or  rust. 

RUST  FORMATION 

Theory.  While  rust  is  largely  or  wholly  oxide  of  iron,  it  is  not 
produced  directly  by  the  contact  of  the  iron  with  the  oxygen  of  the 
air.  The  presence  of  moisture  seems  essential  to  its  formation. 
Much  study  has  been  given  to  the  process  of  rust  formation,  but  the 
reactions  have  not  yet  been  determined  positively.  It  is  quite 
generally  believed  that  electrolytic  action  occurs.  This  theory  is 
well  described  by  Houston  Lowe  in  "Paints  for  Steel  Structures" 
as  follows:* 

"The  electrolytic  theory,  which  no  doubt  has  the  strongest  support,  is 
based  upon  the  recognized  tendency  of  metals  to  go  into  solution,  even  in  pure 
water.  The  act  is  accompanied  by  the  release  of  hydrogen  positively  charged 
with  electricity,  leaving  on  the  metal  a  corresponding  charge  of  negative  elec- 
tricity. If  oxygen  is  at  hand  to  combine  with  the  hydrogen,  the  electrical 
tension  is  relieved  in  an  infinitely  small  current  and  new  portions  of  the  metal 
pass  into  solution ;  otherwise  the  action  is  arrested  by  the  non-conducting  quality 
of  the  thin  film  of  hydrogen. 

"The  presence  of  minute  particles  of  suitable  impurities  in  or  on  the  iron, 
whose  solution  tension  differs  from  the  iron,  or  the  presence  of  acids  in  the  water, 
facilitates  the  discharge  of  the  electric  tension  and,  hence,  the  continuous  re- 
moval of  particles  of  iron  On  the  other  hand,  the  presence  of  alkalies,  and  a  few 
other  substances  that  decrease  hydrogen  ion  concentration,  will  diminish  or 
even  stop  iron  solution  and  rusting  altogether. 

"This,  in  brief,  is  the  substance  of  the  electrolytic  theory  of  rusting,  the 


*John  WUey  &  Sons.  Publishers.  New  York. 


334  STEEL  CONSTRUCTION 

more  complete  explanation  of  which  would  involve  the  details  and  language  of 
the  ionic  theory  of  chemical  action.  Corrosion  of  iron,  in  the  sense  in  which 
that  term  has  been  used  in  this  section,  has  nothing  whatever  to  do  with  elec- 
trolysis by  stray  electrical  currents  from  outside  sources.  The  currents  involved 
in  rusting  under  the  theory  of  electrolytic  action  are  almost  infinitely  short  and 
minute,  a  d  originate  in  or  on  the  metal  itself. 

"The  theory  is  valuable  to  the  extent  that  it  suggests  reasonable  and 
practical  remedy  of  the  defects  either  of  the  metal  or  its  proposed  covering,  or 
both.  As  in  the  treatment  of  diseased  animal  and  plant  tissues,  so  in  this  case, 
intelligent  diagnosis  must  precede  the  application  of  prev5ntives  of  rust.  Ex- 
perimental work  following  the  lines  of  the  electrolytic  theory  in  seeking,  first, 
to  prevent,  or  'inhibit'  corrosion  by  a  priming  coat  and,  secondly,  to  diminish 
the  penetration  of  water  by  suitable  overcoats,  is  promising  good  results,  and  a 
final  solution  of  the  problem  is  confidently  looked  for. 

"The  tendency  of  rust  to  grow  and  spread  out  from  a  center  has  an  adequate 
explanation  in  the  electrolytic  theory.  This  phenomenon  is  especially  per- 
nicious, as  it  results  in  pitting  or,  under  a  paint  coat,  in  a  growth  which  finally 
flakes  off  the  paint  and  exposes  large  areas  of  the  iron." 

Degrees  of  Exposure.  A  piece  of  steel  exposed  to  the  air  will 
ultimately  change  entirely  to  oxide  of  iron  (except  as  to  the  contents 
other  than  pure  iron)  i.  e.,  it  will  be  entirely  destroyed  by  rusting. 
The  rapidity  of  the  change  varies  with  the  conditions  of  exposure. 
The  rusting  will  proceed  very  slowly  if  the  steel  is  kept  in  dry  air; 
less  slowly  if  subjected  occasionally  to  moist  air;  rapidly  if  exposed 
to  moisture  frequently;  and  very  rapidly  if  exposed  to  moisture  in 
the  presence  of  sulphur  or  other  acid  fumes. 

The  first  condition  prevails  when  steel  is  enclosed  in  other 
materials  of  construction,  as  columns  and  beams  enclosed  by  plaster 
in  partitions,  and  in  floor  construction,  so  that  the  moisture  condi- 
tions change  only  slightly.  The  second  condition  applies  when  the 
steel  is  within  the  building,  but  not  encased  in  other  materials,  thus 
being  exposed  to  varying  degrees  of  moisture,  as  unprotected  col- 
umns and  beams  in  storerooms.  The  third  degree  of  exposure 
fairly  represents  unprotected  beams  in  basements,  vaults  under 
sidewalks,  and  steel  work  out  of  doors.  And  the  worst  possible 
exposure,  that  is,  to  moisture  in  the  presence  of  acid  fumes,  is  had 
in  smelters,  and  in  structures  where  the  steel  is  subjected  to  the 
smoke  from  railroad  locomotives. 

Rate  of  Rusting.  Some  studies  have  been  made  of  the  rate 
of  corrosion  under  different  conditions.  It  is  very  evident  that  the 
rate  varies  greatly  with  the  conditions  of  exposure.  Experiments 
along  this  line  have  not  gone  far  enough  to  give  conclusive  results, 


STEEL  CONSTRUCTION  335 

i.e.,  definite  figures  as  to  the  thickness  of  metal  that  will  change  to 
rust  in  a  given  time.  But  it  is  a  matter  of  common  knowledge  that 
there  is  enough  rusting  even  under  the  most  favorable  conditions  to 
make  it  important  that  steel  be  protected. 

Effect  of  Composition  of  Metal.  The  composition  of  the 
metal  lias  some  effect  on  the  rate  of  corrosion.  Structural  steel 
probably  rusts  more  rapidly  than  any  other  form  or  alloy  of  iron. 
Cast  iron  rusts  slowly,  probably  due  to  the  presence  of  graphite, 
which  protects  the  iron.  Wrought  iron  rusts  more  rapidly  than 
cast  iron  and  much  less  rapidly  than  steel.  It  is  believed  that  the 
slag  in  wrought  iron  protects  the  fibers  of  iron  from  exposure  to  the 
air  and  moisture.  The  presence  of  manganese  is  supposed  to  accel- 
erate corrosion,  while  copper  and  other  alloys  retard  it. 

Efforts  have  been  made  to  produce  rust-resisting  metals  by 
two  methods;  by  making  iron  nearly  pure,  and  by  using  an  alloy 
of  copper.  The  -resulting  metals  are  not  rustproof  but  show  much 
slower  rates  of  corrosion  than  ordinary  steel.  Both  have  been 
commercially  successful  as  applied  to  sheet  steel,  but  are  not  yet 
used  for  structural  steel.  Pure  iron  is  not  suitable  for  structural 
purposes  because  of  its  lack  of  strength.  It  is  quite  possible  that 
an  alloy  of  copper  or  other  metal  will  be  developed  for  structural 
steel  that  will  be  nearly  rustproof. 

PAINT 

Purpose.  The  usual  means  employed  to  prevent  corrosion  is 
to  exclude  all  air  and  moisture  from  contact  with  the  metal  by  a 
covering  of  paint.  It  is  desirable  that  the  paint  material  be  such 
as  will  inhibit  the  formation  of  rust,  thus  counteracting  any  imper- 
fections of  the  paint  in  excluding  moisture. 

Qualities.  '  The  following  qualities  are  desirable: 

(1)  Adhesive,  so  that  it  will  hold  fast  to  the  steel. 

(2)  Non-porous,  so  that  it  will  exclude  air  and  moisture. 

(3)  Elastic,  so  that  it  will  not  crack  with  changes  in  tempera- 
ture, or  with  the  deflection  of  the  steel. 

(4)  Hard  at  all  ordinary  temperatures. 

(5)  Non-volatile,  so  that  the  oils  may  not  evaporate  and  leave 
the  inert  materials  of  the  paint  without  a  binder. 

(6)  Not  soluble  in  water. 

(7)  Not  soluble  in  oil,  so  that  it  will   not  soften   when  addi- 
tional coats  are  applied. 


336  STEEL  CONSTRUCTION 

(8)  Inhibit ivc," that  is,  of  such  material  as  will  prevent  the  chem- 
ical or  electrolytic  action  of  rusting. 

(9)  Color  may  be  important. 

Many  of  these  qualities  obviously  are  much  more  important 
on  out-of-door  work  than  on  ordinary  building  work.  No  paint 
has  all  of  these  desirable  qualities,  but  by  using  different  paints  for 
the  several  coats,  the  ideal  conditions  may  be  approximated.  Thus 
the  first  coat  should  be  inhibitive  and  adhesive;  and  the  second  (or 
last  coat,  if  more  than  two  are  used)  should  be  non-porous  and 
should  provide  the  required  wearing  properties. 

Composition.  A  paint  is  made  of  "a  liquid  and  a  solid,  called, 
respectively,  the  "vehicle"  and  the  "pigment". 

Vehicle.  The  best  vehicle  for  paint  is  linseed  oil.  It  may  be 
had  as  raw  oil  or  boiled  oil.  The  latter  is  used  when  quick  drying 
is  desired  but  the  raw  oil  is  believed  to  give  better  results  under 
most  circumstances,  and  especially  with  red  lead/  The  drying  of 
paint  is  accelerated  by  the  use  of  driers  in  the  oil.  A  drier  may  be 
a  volatile  oil,  as  turpentine,  which  effects  its  purpose  by  rapidly 
evaporating  after  the  paint  is  applied;  or  it  may  be  a  japan,  which 
hastens  the  hardening  of  the  oil  and  pigment.  Turpentine  being 
cheaper,  it  is  more  used  than  japans.  The  drier  should  not  exceed 
8  per  cent  of  the  vehicle. 

Linseed  oil  varies  greatly  in  quality  even  when  pure,  and  is 
subject  to  adulterations  which  are  difficult  to  detect.  Some  paint 
makers  claim,  and  probably  justly  so,  that  they  improve  the  vehicle 
by  adding  other  oils  to  the  linseed  oil;  but  in  general- any  additions 
other  than  the  drier  must  be  considered  adulterations. 

Pigments.  Pigments  commonly  used  for  structural  steel  paints 
are  red  lead,  iron  oxide,  graphite,  and  lampblack. 

Red  lead  is  the  red  oxide  of  lead,  Pb3  04,  but  the  red  lead  of 
commerce  contains  a  certain  amount  of  litharge  and  metallic  lead. 
These  elements  cannot  be  entirely  eliminated  on  a  commercial  .basis, 
but  it  is  practicable  to  obtain  a  red  lead  which  is  95  per  cent  pure 
and  it  should  be  so  specified. 

When  mixed  with  linseed  oil,  red  lead  hardens,  much  as  cement 
when  mixed  with  water,  and  forms  a  strong  tenacious  coating.  It 
can  be  made  into  a  heavy  paint,  almost  a  paste,  thus  giving  a  heavy 
coat  on  the  steel,  or  it  can  be  thinned  to  give  a  light  coat.  On 


STEEL  CONSTRUCTION  337 

account  of  its  weight,  red  lead  is  difficult  to  mix  with  oil.  This  is 
especially  true  when  a  large  proportion  of  lead  is  used.  The  maxi- 
mum proportion  is  33  pounds  of  red  lead  to  one  gallon  of  raw  linseed 
oil.  While  this  heavy  mixture  is  desirable,  it  is  expensive  as  to 
labor  and  materials.  A  more  practicable  proportion  is  25  pounds 
of  red  lead  to  one  gallon  of  oil;  a  still  smaller  weight  of  lead  is  often 
used  and  will  invariably  be  used  unless  the  proportions  required 
are  definitely  specified,  for  there  is  no  standard  practice  to  govern 
it.  Red  lead  paint  with  a  small  proportion  of  red  lead  can  be  mixed 
by  hand,  but  if  the  amount  of  lead  is  as  much  as  25  pounds,  the 
mixing  should  be  done  in  a  churn,  or  ground  into  the  oil  at  the  paint 
factory. 

On  account  of  its  weight  and  its  settling  qualities,  it  has  not 
been  practicable,  heretofore,  to  keep  red  lead  paint  for  any  length  of 
time,  as  the  lead  settles  to  the  bottom  and  hardens.  The  hardening 
quality  seems  to  be  due  largely  to  the  litharge.  Now  that  the  lith- 
arge can  be  eliminated  from  the  red  lead,  it  is  practicable  to  keep 
the  ready-mixed  paint  for  a  much  longer  period.  It  can  now  be 
obtained  from  the  paint  manufacturers  ground  into  the  oil,  forming 
a  thick  paste,  which  can  be  thinned  to  the  proper  consistency  by 
the  addition  of  oil  when  it  is  to  be  used.  The  thinning  can  be 
gaged  by  the  weight  of  the  finished  paint  on  the  following  basis: 

A  wreight  of  24.43  pounds  for  the  finished  paint  corresponds  to 
25  pounds  of  lead  to  one  gallon  of  oil. 

A  weight  of  25.92  pounds  corresponds  to  28  pounds  of  lead  to 
one  gallon  of  oil. 

A  weight  of  26.76  pounds  corresponds  to  30  pounds  of  lead  to 
one  gallon  of  oil. 

A  weight  of  27.10  pounds  corresponds  to  33  pounds  of  lead  to 
one  gallon  of  oil.  (These  values  are  taken  from  a  circular  issued  by 
the  National  Lead  Company.). 

A  ready-mixed  red  lead  paint  can  be  made  by  substituting  for 
a  part  of  the  red  lead  some  other  pigment  of  inert  material  which 
will  retard  the  settling,  and  harden.  Lampblack,  asbestine,  and 
mica  are  sometimes  used  for  this  purpose.  Such  paints  usually 
contain  less  than  15  pounds  of  red  lead  per  gallon  of  oil,  and  are 
much  less  satisfactory  than  the  red  lead  paste. 

Iron  oxide,  commercially  available,  varies  greatly  in  weight  and 
physical  characteristics.  Some  is  taken  direct  from  mines  but  most 


338  STEEL  CONSTRUCTION 

of  it  is  manufactured.  It  does  not  have  any  cementing  properties 
when  mixed  with  linseed  oil  so  must  be  held  in  place  by  the  oil. 
The  paint  will  last  only  as  long  as  the  oil  binder  remains  intact. 
The  iron  oxide  does  not  inhibit  corrosion  but  under  some  circum- 
stances accelerates  it,  -thus  leading  'to  the  formation  of  patches  of 
rust  under  the  paint.  Under  favorable  conditions  it  makes  a  good 
protective  coating.  Iron  oxide  is  mixed  with  boiled  linseed  oil, 
using  about  8  pounds  of  the  pigment  to  one  gallon  of  oil. 

The  carbon  paints,  which  include  lampblack  and  graphite,  have 
no  cementing  properties  when  mixed  with  oil.  The  amount  of 
pigment  used  is  small  compared  with  that  used  in  red  lead  paint. 
It,  therefore,  has  much  greater  spreading  power  and  consequently 
makes  a  much  thinner  film.  As  it  does  not  inhibit  corrosion,  its 
protective  power  depends,  entirely  on  the  oil,  making  it  necessary  to 
use  several  coats  in  order  to  get  satisfactory  results.  It  makes  a 
satisfactory  second  coat  over  red  lead.  The  carbon  pigments, 
particularly  graphite,  are  subject  to  many  adulterations.  There  are 
no  standard  proportions.  Carbon  paints  can  be  made  at  the  factory 
and  will  keep  for  an  indefinite  period. 

Prepared  Paints.  Many  proprietary  paints  are  offered  for 
structural  steel.  Some  have  much  merit,  others  none.  They  should 
not  be  used  unless  there  are  authentic  records  of  successful  use-. 

Painting  Required.  Structural  steel  in  buildings  is  protected 
from  moisture  by  being  enclosed  by  other  materials.  On  the  other 
hand,  in  most  cases  it  cannot  be  repainted,  so  the  original  painting 
is  of  great  importance.  The  writer  recommends  painting  it  two 
coats,  first  red  lead,  second  graphite  or  lampblack.  If  the  steel  is 
to  be  encased  in  concrete,  the  second  coat  may  be  omitted,  the  con- 
crete furnishing  as  much  protection  as  the  second  coat  of  paint. 

Cleaning.  The  paint  can  have  no  mechanical  bond  to  the 
steel  so  must  depend  on  adhesion  to  hold  it  in  place.  This  makes  it 
necessary  that  the  surfaces  be  cleaned  before  painting,  removing  all 
rust,  dirt,  grease,  and  mill  scale.  The  cleaning  is  of  utmost  impor- 
tance, for  if  not  done  thoroughly,  the  paint  will  not  adhere;  and,  if 
rusting  has  already  started,  it  may  continue  under  the  paint.  It 
is  not  uncommon  to  find  large  patches  of  rust  over  which  the  paint 
remains  unbroken.  This  is  apt  to  occur  when  the  surface  is  not 
properly  cleaned  before  repainting. 


STEEL  CONSTRUCTION  339 

The  most  effective  way  of  cleaning  steel  is  by  means  of  the 
sand  blast.  This  method  is  expensive  and  is  not  much  used  for 
steel  work  for  buildings.  It  is  used  chiefly  for  cleaning  old  steel 
work,  especially  bridges,  for  repainting.  The  usual  means  of  cleaning 
is  by  the  use  of  the  scraper,  chisel,  and  wire  brush.  This  work  can 
be  well  done  with  tto?se  tools,  if  enough  labor  is  expended  on  it. 

Applying  the  Paint.  The  paint  is  best  applied  with  heavy 
round  brushes.  It  must  be  spread  evenly  and  cover  the  entire 
surface  and  be  worked  into  all  corners  and  joints.  The  metal  surfaces 
should  be  warm  and  free  from  moisture.  In  cold  weather  the  paint 
should  be  warmed. 

Surfaces  in  Contact.  It  is  customary  to  specify  that  surfaces 
which  will  be  in  contact  after  assembling  shall  be  painted  before 
assembling.  The  desirability  of  this  has  been  questioned  on  the 
basis  that  the  paint  is  probably  destroyed  by  the  heat  from  the 
rivets.  Nevertheless,  there  is  no  evidence  that  such  painting  does 
any  harm  and  it  is  best  to  do  it  in  accordance  with  usual  practice. 
Box  sections,  such  as  channel  columns,  should  have  two  coats  on 
the  inner  surfaces  before  assembling." 

Cement  as  a  Rust  Preventive.  Portland  cement  mortar  and 
concrete  are  inhibitors  of  rust  and,  if  dense  and  in  actual  contact 
with  the  metal,  provide  the  necessary  protection  against  moisture. 
If  applied  to  clean  steel  surfaces,  no  other  protection  is  required. 
But  the  steel,  if  not  painted  at  the  shop,  usually  will  become  badly 
rusted  before  it  is  enclosed  in  the  building,  making  it  desirable  that 
the  shop  coat  of  paint  be  used.  Then  the  concrete  casing  will 
make  it  unnecessary  to  apply  the  second  coat  of  paint. 

PROTECTION  FROM  FIRE 

Effects  of  Heat  on  Steel.  Expansion.  Heat  applied  to  steel 
causes  it  to  expand.  Its  coefficient  of  expansion  is  0.0000067  for 
one  degree  Fahrenheit,  that  is,  for  each  increase  of  one  degree  in 
temperature  a  unit  of  length  increases  by  the  amount  of  the  coeffi- 
cient. Thus  for  an  increase  of  100  degrees  in  temperature,  the 
increase  for  each  unit  of  length  is  100X0.0000067  =  0.00067;  for  a 
length  of  18  feet,  the  total  increase  in  length  is  0.00067x18  = 
0.01206  feet,  or  .14472  inches. 


340  STEEL  CONSTRUCTION 

There  is  a  corresponding  change  in  the  opposite  direction,  if 
the  temperature  decreases.  From  this  it  is  clear  that  expansion  and 
contraction  due  to  changes  in  temperature  occur  in  appreciable 
amount.  The  longer  the  member,  or  series  of  members,  the  greater 
the  change  in  length.  Within  buildings,  the  change  in  temperature 
ordinarily  is  not  enough  to  cause  trouble,  but  if -the  steel  is  exposed 
to  fire,  it  might  expand  enough  to  push  a  wall  out  of  place  even 
though  not  heated  enough  to  affect  its  strength.  Cases  have  occurred 
where  walls  have  been  seriously  displaced  by  ordinary  changes  of 
temperature,  because  the  expansion  of  the  steel  pushed  the  wall 
outward,  whereas  the  succeeding  contraction  did  not  pull  it  back; 
then  the  next  expansion  pushed  it  farther  out,  and  thus  by  succes- 
sive movements  the  wall  was  pushed  farther  and  farther  out  of  place. 

Loss  of  Strength.  Experiments  indicate  that  steel  can  be  heated 
to  a  temperature  of  about  600  degrees  Fahrenheit  before  it  begins 
to  lose  strength.  At  Righer  temperatures,  it  loses  strength  rapidly 
and  will  fail  of  its  own  weight  at  a  temperature  of  about  1500  de- 
grees. Steel  melts  at  2500  degrees  (approx.). 

Intensity  of  Heat  in  a  Fire.  The  intensity  of  heat  developed 
in  a  fire  varies  greatly  according  to  conditions.  Many  cases  are 
recorded  showing  steel  bent  into  a  tangled  mass  from  the  burning 
of  a  building,  indicating  temperatures  of  1500  degrees  or  more. 
Such  temperatures  can  be  produced  by  burning  the  wood  framework 
of  an  ordinary  building,  or  even  the  contents  of  a  fireproof  building. 

Protective  Methods.  Unprotected  steel  yields  very  quickly  in 
a  fire,  much  more  quickly  than  wood  beams  of  the  same  strength. 
It  is  dangerous  and  inexcusable  to  use  structural  steel  in  a  building 
without  providing  for  its  safety.  Steel  is  protected  from  fire  by 
encasing  it  in  a  fireproof  material.  Almost  any  material  encasing 
steel  will  protect  it  to  some  extent.  Even  a  tight  casing  of  wood 
will  protect  it  for  a  little  while  in  a  fire.  Ordinary  plaster  on  wood 
lath  will  protect  it  only  until  the  fire  gets  through  the  plaster,  after 
which  the  burning  of  the  lath  aids  in  the  destruction  of  the  steel. 
Cement  plaster  on  metal  lath  is  efficient  only  to  a  limited  degree, 
and  while  it  is  an  incombustible  material,  it  is  not  fireproof  within 
the  meaning  of  that  term  as  used  in  building  construction. 

Misuse  of  the  Term  Fireproof.  Many  buildings  are  called  fire- 
proof when  the  protection  of  the  steel  is  nothing  more  than  described 


STEEL  CONSTRUCTION  341 

above.  Instances  can  be  cited  of  hotels  advertised  as  fireproof  with 
steel  beams  placed  among  wood  joists  with  no  protection  whatever. 
Amount  of  Protection  Depends  on  Conditions.  A  building  may 
be  made  entirely  of  incombustible  material  and  still  not  be  fireproof, 
if  the  steel  is  not  encased  to  protect  it  from  the  contents  of  the 


Fig.  209.     Brick  and  Concrete  Arch  Construction  Showing  Partial 
Protection  for  I-Beams 

building.  Fig.  209  illustrates  a  form  of  construction  of  this  sort 
which  was  much  used  a  number  of  years  ago.  The  brick  arches 
and  the  concrete  filling  protect  the  beam  except  on  the  bottom 
flange,  which  is  left  exposed  to  fire  from  the  burning  of  the  contents 
of  the  room  below.  Fig.  210  is  a  similar  form  of  construction  in 
which  a  corrugated-steel  arch  replaces  the  brick  arch.  This  partial 
protection  is  of  some  value,  but  it  is  so  easy  under  present  methods 
.to  get  complete  protection  that  these  forms  are  no  longer  used. 

On  the  other  hand,  a  building  having  no  combustible  material 

^£<^;*.'&t*-:<^*^*%i?s<£.^.  _xtt2£&ff&& 

f^g&SS^- 

££=="  ^^^^^gjggjglll^S 

COR  RUG  A  TED   IRQH  APCH  CO/i5TQUCT/OM 

Tig.  210.      Corrugated  Iron  and  Concrete  Arch  Construction  Showing 
Insufficient  Protection  for  I-Beams 

in  its  construction  or  contents,  and  having  no  external  hazard,  need 
not  have  its  steel  framework  fireproofed.  A  foundry  building  or  a 
machine  shop  may  be  such  a  case. 

Standard  Specifications.  Steel  to  be  really  fireproofed  must  be 
entirely  encased  in  a  fireproof  material.  The  material  must  be 
such  that  it  will  conduct  heat  very  slowly  and  that  it  will  maintain 
its  integrity  when  subjected  to  a  fire  of  the  greatest  in  tensity  and 
longest  duration  likely  to  occur,  and  when  subjected  to  a  stream  of 
water  from  a  fire  hose  while  at  its  maximum  heat. 

The  "Standard  Test  for  Fireproof  Floor  Construction"  adopted 
by  the  American  Society  for  Testing  Materials*  requires: 

•American  Society  for  Testing  Materials,  Edgar  Marburg.  Secretary,  University  of  Penn- 
sylvania, Philadelphia. 


342  STEEL  CONSTRUCTION 

"No  plastering  shall  be  applied  to  the  underside  of  the  floor  construction 
under  test. 

"The  floor  shall  be  subjected  for  four  hours  to  the  continuous  heat  of  a  fire 
of  an  average  temperature  of  not  less  than  1700°  F. ,  the  fuel  used  being  either 
wood  or  gas,  so  introduced  as  to  cause  an  even  distribution  of  heat  throughout 
the  test  structure. 

"The  heat  obtained,  shall  be  measured  by  means  of  standard  pyrometers, 
under  the  direction  of  an  experienced  person.  The  type  of  pyrometer  is  immater- 
ial so  long  as  its  accuracy  is  secured  by  proper  standardization.  The  heat 
should  be  measured  at  not  less  than  two  points  when  the  main  floor  span  is  not 
more  than  10  feet  and  one  additional  point  when  it  exceeds  10  feet.  Tempera- 
ture  readings  at  each  point  are  to  be  taken  every  three  minutes.  The  heat 
determination  shall  be  made  at  points  directly  beneath  the  floor  so  as  to  secure 
a  fair  average. 

"At  the  end  of  the  heat  test  a  stream  of  water  shall  be  directed  against  the 
underside  of  the  floor,  discharged  through  a  1 1-inch  nozzle,  being  held  at  more 
than  3  feet  from  the  firing  door  during  the  application  of  the  water."1 

Material  which  will  withstand  this  test  is  suitable  for  fireproofing 
steel  in  any  part  of  a  building. 

Fireproof  Materials.  Cinder  Concrete.  Cinder  concrete  has 
been  used  extensively  for  fireproofing  but  it  is  not  altogether  satis- 
factory. It  is  difficult  to  get  cinders  free  from  unburned  coal,, 
ashes,  and  refuse.  Sulphur  in  the  cinders  causes  rusting  of  the 
steel.  Its  use  is  not  warranted  on  first-class  work. 

Portland  Cement  Concrete.  Portland  cement  concrete,  made 
of  crushed  stone  or  gravel,  is  an  excellent  fireproofing  material.  It 
has  the  necessary  resistance  to  fire  and  water,  prevents  rusting  of 
the  steel,  and  in  many  situations  adds  to  the  strength  of  the  steel 
member.  If  its  surface  is  left  rough  or  is  roughened  after  the 
forms  are  removed,  plaster  will  stick  to  it. 

When  subjected  to  a  fire,  the  concrete  is  damaged.  The  depth 
of  the  injury  may  be  as  much  as  1J  inches,  depending  on  the  quality 
of  the  concrete  and  the  kind  of  stone  used  in  it.  The  better  the 
concrete,  the  less  it  is  injured  by  the  heat.  Heat  calcines  limestone 
and  disintegrates  granite,  so  that  these  stones  are  not  as  suitable 
for  fireproofing  purposes  as  hard  sandstones,  trap,  and  other  stones 
not  so  easily  affected  -by  heat.  An  excellent  concrete  for  fireproofing 
can  be  made  from  crushed  tile  and  brick.  On  buildings  where  tile 
is  used  for  floor  arches  and  partitions,  the  broken  pieces  can  be 
crushed  and  used  for  fireproofing  the  columns  and  any  other  mem- 
bers not  protected  by  the  tile  floor  arches. 


STEEL  CONSTRUCTION 


343- 


Concrete  which  has  been. damaged  by  fire  does  not  lose  its 
property  of  non-conductivity,  consequently  it  is  efficient  as  fire- 
proofing  so  long  as  it  remains  in  place;  although  it  has  lost  its 
strength,  it  usually  will  remain  in  place  until  removed  by  some  me- 
chanical means,  as  the  application  of  a  stream  of  water.  After  a 
fire,  the  damaged  concrete  must  be  removed  and  replaced. 

Concrete  is  placed  around  steel  by  building  forms  around  the 
members  and  pouring  concrete  into  them,  Fig.  211.  Wire  mesh  or 
expanded  metal  should  be  attached  to  the  bottom  flanges  of  beams 
and  wrapped  around  columns  to  provide  a  mechanical  bond  for  the 
concrete  so  that  it  will  not  fall  off  during  or  after  a  fire. 


Fig  .211.    I-Beam  and  Coliifnn  Sections  Showing  Concrete  Fireproofing. 

Hollow  Tile.  Hollow  tile  is  molded  from  clay  and  baked  at  a 
high  temperature.  The  clay  used  must  be  such  that  it  will  not 
warp,  or  fuse  in  the  kiln.  It  is  desirable  that  the  tile  be  porous  and 
tough  rather  than  dense  and  brittle.  The  tile  is  made  porous  by 
mixing  sawdust  with  the  clay.  This  burns  out  during  the  baking, 
leaving  voids  and  producing  the  desired  porosity.  Dense  tile  and 
tile  which  is  glazed  is  likely  to  shatter,  if  exposed  to  a  stream  of 
water  when  hot,  thus  making  it  useless  for  fire  protection;  further- 
more, plaster  does  not  adhere  to  it  as  well  as  to  porous  tile. 

The  tile  is  made  hollow  to  save  weight,  and  to  provide  air 
spaces  which  are  insulators  against  both  heat  and  moisture. 

This  material  is  molded  into  a  great  variety  of  shapes  to  suit 
the  various  requirements  of  the  steel  members  to  be  protected. 
Certain  shapes  are  practically  standard;  special  shapes  can  be  had 
only  when  required  in  large  quantity. 

Figs.  212,  213,  214,  and  215  show  a  number  of  illustrations  of 
tile  fireproofing  of  joists,  girders,  spandrels,  and  columns.  The 


344 


STEEL  CONSTRUCTION 


joists  are  usually  fireproofed  by  the  skewbacks  of  the  floor  arches. 
On  other  members  the  tile  serves  only  for  fireproofing  and  for  furnish- 


Fig.  212.     Method  of  Fireproofiing  Joists  in  Connection  with  Flat  Tile  Floor  Arch 

ing  a  surface  for  plastering.    It  can  be  used  for  fireproofing  steel 
members  in  almost  any  situation. 

Tile  is  set  in  mortar  in  the  same  manner  as  bricks  are  laid. 
Any  space  between  the  tile  and  the  steel  should  be  filled  with  Port- 


Fig.  213.    Sections  Showing  Method  of  Fireproofing  Beams 


land  cement  mortar.  A  heavy  layer  of  mortar  should  be  plastered 
on  the  webs  of  beams  before  setting  skewbacks  or  other  tiles  against 
them. 


Fig.  214.    Sections  Showing  Method  of  Fireprcofing  Spandrels 


346 


STEEL  CONSTRUCTION 


Fireproofing  tile  must  be  designed  to  be  securely  supported  by 
the  steel.  Steel  clips  or  wire  must  be  used  in  some  situations. 
Thus  the  column  casing  should  be  held  in  place  by  copper  wire 
bands  unless  it  is  securely  held  by  interlocking  of  the  tile.  Soffit 
tile  on  joists  and  girders  require  metal  clips  or  woven  wire  fabric  to 
hold  them  in  place  even  though  they  appear  to  have  support  from 
shoe  tile  or  other  adjacent  members. 

Tile  has  considerable  strength  in  compression  and  may  be  so 
used,  but  should  not  be  subjected  to  other  stresses. 

Brick.  Brick  masonry  is  an  excellent  fireproofing  material  so 
far  as  its  resistance  to  heat  is  concerned.  However,  it  is  not  easily 


Fig.  215.     Sections  Showing  Method  of  Fireproofing  Columns  with  Tile  and  Concrete 

.supported  and,  therefore,  is  not  generally  available  for  this  purpose 
on  beams,  but  in  some  cases ^it  can  be  used  to  good  advantage  for 
e.ncasing  columns. 

Selection  of  Fireproofing.  Portland  cement  concrete  and  hollow 
tile  are  the  materials  best  suited  for  fireproofing.  Both  are  efficient 
for  this  purpose.  The  choice  between  them  is  usually  governed 
by  other  considerations,  chief  of  which  is  the  type  of  floor  construc- 
tion, which  in  turn  may  be  determined  by  cost  or  some  other  con- 
sideration. If  the  floor  is  to  be  of  reinforced  concrete,  concrete  will 
be  used  for  fireproofing  the  steel  framework.  If  the  floor  is  to  be  of 
tile  arch  construction,  that  material  will  be  used  for  fireproofing; 
but  even  in  this  case  concrete  can  be  used  advantageously  for  the 
columns. 

Thickness  of  Fireproofing.  The  thickness  of  the  covering 
required  to  furnish  the  desired  protection  varies  with  the  situation 
and  the  importance  of  the  member.  Columns  being  vital  to  the 
support  of  the  building  are  given  the  most  protection.  Lintels  and 
spandrel  girders  are  subject  to  severe  exposure  and  are  given  about 


STEEL  CONSTRUCTION  347 

the  same  protection  as  columns.  Joists  and  girders  are  local  mem- 
bers and  not  so  heavily  fireproofed.  The  top  flanges  of  beams  and 
girders  do  not  need  as  much  protection  as  the  bottom  flanges. 

The  requirements  in  Chicago  are:* 

Columns — Exterior,  (a)  All  iron  or  steel  used  as  vertical  supporting 
members  of  the  external  construction  of  any  building  exceeding  fifty  feet  in  height 
shall  be  protected  against  the  effects  of  external  change  of  temperature  and  of 
fire  by  a  covering  of  fireproof  material  consisting  of  at  least  four  inches  of  brick, 
hollow  terra  cotta,  concrete,  burnt  clay  tiles,  or  of  a  combination  of  any  two  of 
these  materials,  provided  that  their  combined  thickness  is  not  less  than  four 
inches.  The  distance  of  the  extreme  projection  of  the  metal,  where  such  metal 
projects  beyond  the  face  of  the  column,  shall  be  not  less  than  two  inches  from  the 
face  of  the  fireproofing;  provided,  that  the  inner  side  of  exterior  columns  shall  be 
fireproofed  as  hereafter  required  for  interior  columns. 

(b)  Where  stone  or  other  incombustible  material  not  of  the  type  defined 
in  this  ordinance  as  fireproof  material  is  used  for  the  exterior  facing  of  a  building, 
the  distance  between  the  back  of  the  facing  and  the  extreme  projection  of  the 
metal  of  the  column  proper  shall  be  at  least  two  inches,  and  the  intervening 
space  shall  be  filled  with. one  of  the  fireproof  materials. 

(c)  In  all  cases,  the  brick,  burnt  clay,  tile,  or  terra  cotta,  if  used  as  a  fire- 
proof covering,  shall  be  bedded  in  cement  mortar  close  up  to  the  iron  or  steel 
members,  and  all  joints  shall  be  made  full  and  solid. 

Columns — Interior,  (a)  Covering  of  interior  columns  shall  consist  of 
one  or  more  of  the  fireproof  materials  herein  described. 

(b)  If  such  covering  is  of  brick  it  shall  be  not  less  than  four  inches  thick; 
if  of  concrete,  not  less  than  three  inches  thick;  if  of  burnt  clay  tile,  such  covering 
shall  be  in  two  consecutive  layers,  each  not  less  than  two  inches  thick,  each 
having  one  air  space  of  not  less  than  one-half  inch,  and  in  no  such  burnt  clay  tile 
shall  the  burnt  clay  be  less  than  five-eighths  of  an  inch  thick;  or  if  of  porous  clay 
solid  tiles,  it  shall  consist  of  at  least  two  consecutive  layers,  each  not  less  than 
two  inches  thick;  or  if  constituted  of  a  combination  of  any  two  of  these  materials, 
one-half  of  the  total  thickness  required  for  each  of  the  materials  shall  be  applied, 
provided  that  if  concrete  is  used  for  such  layer  it  shall  not  be  less  than  two  inches 
thick. 

(c)  In  the  case  of  columns  having  an  "H"  shaped  cross  section  or  ot 
columns  having  any  other  cross  section  with  channels  or  chases  open  from  base 
plates  to  cap  plates  on  one  or  more  sides  of  the  columns,  then  the  thickness  of 
the  fireproof  covering  may  be  reduced  to  two  and  one-half  inches,  measuring 
in  the  direction. in  which  the  flange  or  flanges  project,  and  provided  that  the 
thin  edge  in  the  projecting  flange  or  arms  of  the  cross  sections  does  not  exceed 
three-quarters  of  an  inch  in  thickness      The  thickness  of  the  fireproof  covering 
on  all  surfaces  measuring  more  than  three-quarters  of  an  inch  wide  and  measur- 
ing in  a  direction  perpendicular  to  such  surfaces  shall  be  not  less  than  that 
specified  for  interior  columns  in  the  beginning  of  this  section,  and  all  spaces, 
including  channels  or  chases  between  the  fireproof  covering  and  the  metal  of 
the  columns,  shall  be  filled  solid  with  fireproof  material.     Lattice  or  other  open 
columns  shall  be  completely  filled  with  approved  cement  concrete. 

'Revised  Building  Ordinances  of  the  City  of  Chicago  as  amended  Feb.  20.  1911. 


348  STEEL  CONSTRUCTION 

Columns — Wiring  Clay  Tile  On.  (a)  Burnt  clay  tile -column  covering 
shall  be  secured  by  winding  wire  around  the  columns  -after  the  tile  has  all  been 
set  around  such  columns.  The  wire  shall  be  securely  wound  around  tile  in  such 
manner  that  every  tile  is  crossed  at  least  once  by  a  wire.  If  iron  or  steel  wire  is 
used  it  shall  be  galvanized  and  no  wire  used  shall  be  less  than  -number  twelve 
gage.  ******** 

Pipes  Enclosed  by  Covering,  (a)  Pipes  shall  not  be  enclosed  in  the  fire- 
proofing  of  columns  or  in  the  fireproofing  of  other  structural  members  of  any 
fireproof  building;  provided,  however,  gas  or  electric  light  conduits  not  exceeding 
one  inch  diameter  may  be  inserted  in  the  outer  three-fourths  inch  of  .the  fire- 
proofing  of  such  structural  member,  where  such  fireproofing  is  entirely  composed 
of  concrete. 

(b)  Pipes  or  conduits  may  rest  upon  the  tops  of  the  steel  floor  beams  or 
girders,  provided  they  are  imbedded  in  cinder  concrete  to  which  slaked  lime 
equal  to  five  per  cent  of  the  volume  of  concrete  has  been  added  before  mixing 
or  their  being  imbedded  in  stone  concrete. 


Spandrel  Beams,  Girders,  Lintels.  The  metal  of  the  exterior  side  of  the 
spandrel  beams  or  spandrel  girders  of  exterior  walls,  or  lintels  of  exterior  walls, 
which  support  a  part  of  exterior  walls,  shall  be  covered  in  the  same  manner,  and 
with  the  same  material  as  specified  for  the  exterior  columns  in  this  chapter; 
provided,  however,  that  shelf  angles  connected  to  girders  by  brackets  or  pro- 
jections of  girder  flanges  not  figured  as  part  of  the  flange  section  may  come 
within  two  inches  of  the  face  of  the  brick  or  other  covering  of  such  spandrel 
beams,  girders,  or  lintels.  The  covering  thickness  shall  be  measured  from  the 
extreme  projection  of  the  metal  in  every  case. 

Beams,  Girders  and  Trusses — Coverings  of.  (a)  The  metal  beams, 
girders,  and  trusses  of  the  interior  structural  parts  of  a  building  shall  be  covered 
by  one  of  the  fireproof  materials  hereinbefore  specified,  so  applied  as  to  be  sup- 
ported entirely  by  the  beam  or  girder  protected,  and  shall  be  held  in  place  by 
the  support  of  the  flan  eras  of  such  beams  or  girders  and  by  the  cement  mortar 
used  in  setting. 

(b)  If  the  covering  is  of  brick,  it  shall  be  not  less  than  four  inches  thick; 
if  of  hollow  tiles  or  if  of  solid  porous  tiles  or  if  of  terra  cotta,  such  tiles  shall  be 
not  less  than  two  inches  thick,  applied  to  the  metal  in  a  bed  of  cement  mortar; 
hollow. tiles  shall  be  constructed  in  such  a  manner  that  there  shall  be  one  air 
.space  of  at  least  three-fourths  of  an  inch  by  the  width  of  the  metal  surface  to  be 
covered  within  such  clay  coverings;  the  minimum  thickness  of  concrete  on  the 
bottom  and  sides  of  metal  shall  be  two  inches. 

(c)  The  top  of  all  beams,  girders,  and  trusses  shall  be  protected  with  not 
less  than  two  inches  of  concrete  or  one  inch  of  burnt  clay  bedded  solid  on  the 
metal  in  cement  mortar. 

(d)  In  all  cases  of  beams,  girders,  or  trusses,  in  roofs  or  floors,  the  pro- 
tection of  the  bottom  flanges  of  the  beams  and  girders  and  as  much  of  the  web 
of  the  same  as  is  not  covered  by  the  arches  shall  be  made  as  hereinbefore  specified 
for  the  covering  of  beams  and  girders.     In  every  case  the  thickness  of  the  cover- 
ing shall  be  measured  from  the  extreme  projection  of  the  metal,  and  the  entire 
space  or  spaces  between  the  covering  and  the  metal  shall  be  filled  solid  with  one 
of  the  fireproof  materials,  excepting  the  air  spaces  in  hollow  tile. 


STEEL  CONSTRUCTION  349 

(e)  Provided,  however,  that  all  girders  or  trusses  when  supporting  loads 
from  more  than  one  story  shall  be  fireproofed  with  two  thicknesses  of  fireproof 
material  or  a  combination  of  two  fireproof  materials  as  required  for  exterior 
columns,  and  each  covering  of  fireproof  material  shall  be  bedded  solid  in  cement 
mortar. 

Fireproofing  of  Exterior  Sides  of  M  ullions.  In  buildings  required  by  this 
chapter  to  be  of  fireproof  construction  on  exposures  where  metal  frames,  doors, 
sash,  and  wire  glass  are  not  required,  all  vertical  door  or  window  mullions  over 
eight  inches  wide  shall  be  fae*ed  with  incombustible  material,  and  horizontal 
transom  bars  over  six  inches  wide  shall  be  faced  with  a  fireproof  or  with  an  incom- 
bustible material. 

Iron  or  Steel  Plates  for  Support  of  Wall.  Where  iron  or»steel  plates  or 
angles  are  used  in  each  story  for  the  support  of  the  facings  of  the  walls  of  such 
story,  such  plates  or  angles  shall  be  of  sufficient  strength  to  carry  the  weight 
within  the  limits  of  fiber  stress  for  iron  and  steel  elsewhere  specified  in  this 
chapter  of  the  enveloping  material  for  such  story,  and  such  plates  or  angles  may 
extend  to  within  two  inches  of  the  exterior  of  such  covering. 

SPECIFICATIONS 

Purpose.  The  purpose  of  specifications  is  to  give  a  detailed 
description  of  such  features  of  the  work  as  can  thus  be  given  more 
clearly  or  be  more  easily  defined  than  on  drawings.  They  must 
co-operate  with  and  supplement  the  drawings,  but  should  not  repeat 
the  data  given  on  the  drawings,  for  every  repetition  is  an  added 
opportunity  for  conflict  or  error. 

In  addition  to  the  technical  requirements  referred  to  above, 
the  specifications  usually  include  certain  items  more  related  to  the 
business  transaction  between  the  purchaser  and  the  contractor. 

The  specifications  prepared  by  the  designer  are  to  be  used  for 
the  guidance  of  the  contractor  in  estimating  the  value  of  the  work, 
of  the  mill  in  rolling  the  steel,  of  the  engineer  in  preparing  working 
drawings,  and  of  the  fabricating  shop  in  manufacturing  the  material. 
These  purposes  should  be  kept  in  mind  in  writing  specifications. 

The  relation  of  the  specifications  to  the  contract  should  be 
clearly  understood.  In  all  cases  the  specifications  should  be  made 
a  part  of  the  contract  and  they  are  then  just  as  binding  as  if  written 
into  the  contract.  This  indicates  the  importance  of  having  them 
correctly  written.  As  far  as  practicable,  items  in  the  specifications 
should  not  be  repeated  in  the  contract  and,  on  the  other  hand,  items 
which  belong  in  the  contract  should  not  be  in  the  specifications, 
for  such  repetitions  lead  to  conflicting  or  ambiguous  provisions. 


350  STEEL  CONSTRUCTION 

GENERAL  CHARACTERISTICS 

A  number  of  proposed  standard  specifications  for  structural 
steel  have  been  published.  Usually  their  purpose  is  more  for  the 
guidance  of  the  designer  than  of  the  contractor.  Some  of  them 
cover  both  purposes  quite  fully.  Such  a  one  is  "Revised  General 
Specifications  for  Structural  Work  for  Buildings"  by  C.  C.  Schneider, 
M.  Am.  Soc.,  C.  E.,  published  in  the  Transactions  of  the  American 
Society  of  Civil  Engineers,  Vol.  LIV,  page  490.  This  is  referred  to 
as  Schneider's  Specifications.  It  can  be  used  in  whole  or  in  part 
in  making  up  specifications  for  a  particular  work.  It  is  published 
and  for  sale  by  the  Engineering  News  Publishing  Company,  so  that 
copies  are  readily  available.  Consequently,  in  using  the  specifi- 
cations, the  parts  desired  need  not  be  copied  but  can  be  referred  to 
by  subject  and  paragraph  number.  Considerable  portions  are 
quoted  in  the  specifications  given  later. 

When  such  general  specifications  are  used,  they  must  be  supple- 
mented to  provide  for  the  special  requirements  of  the  work  and  for 
the  business  features  before  mentioned. 

Outline  for  Specifications.  Complete  specifications  should 
include  the  following  subjects: 

Instructions  to  Bidders  Quality  of  Materials 

General  Conditions  Details  of  Construction 

Scope  of  Work  Workmanship 

Loads  Painting 

Unit  Stresses  Inspection 

Erection 

Instructions  to  Bidders.  This  is  entirely  a  business  feature  and 
may  be  made  a  separate  document  from  the  specifications.  But  if 
so,  it  should  accompany  the  specifications  which  are  sent  to  bidders. 
As  the  instructions  may  contain  items  which  might  later  affect  the 
interpretation  of  the  contract,  it  is  best  that  they  be  included  in 
the  specifications  and  thus,  automatically,  become  a  part  of  the 
contract. 

The  instructions  give  the  time  and  place  for  submitting  bids, 
the  price  basis,  and  any  other  directions  pertinent  to  the  case  in 
hand.  Bidders  may  be  required  to  state  the  length  of  time  required 
by  them,  if  this  will  be  a  consideration  in  letting  the  contract. 


STEEL  CONSTRUCTION  351 

General  Conditions.  The  general  conditions  have  no  very 
direct  relation  to  the  technical  requirements  but  are  more  clearly 
business  features.  They  cover  such  items  as  bonds,  liability  insur- 
ance, watchman  service,  etr. 

Scope  of  Work.  This  section  of  the  specifications  is  devoted  to 
the  particular  work  under  consideration  and  should  be  most  care- 
fully stated,  for  it  governs  the  amounts  of  material  and  service  to 
be  furnished.  The  paragraphs  should  cover  the  following  items: 

(a)  Describe  definitely  the  work  included.     If  separate  draw- 
ings are  made  for  the  structural  steel  and  show  completely  all  the 
material  to  be  furnished,  the  work  may  be  so  described.     But  if 
the  structural  steel   is  shown  on  drawings  with  other  materials, 
particularly  ornamental  or  miscellaneous  iron,  then  the  description 
must  be  given  in  sufficient  detail  to  make  it  perfectly  clear.    .It  must 
be  understood  that  the  term  "structural  steel"  is  not  definite  enough 
to  be  used  without  such  a  description  as  required  above,  for  struc- 
tural shapes  may  be  used  in  stair  construction,  for  furring,  for  win- 
dow frames,  and  in  other  situations,  when  it  is  desirable  that  such 
items  be  furnished  .by  other  contractors.     Cast-iron  pedestals  for 
steel  columns  and  cast-iron  columns,  if  used,  are  usually  included  in 
the  contract  with  the  structural  steel. 

(b)  Identify  the  drawings  involved  by  numbers  and  dates. 

(c)  State  the  place  of  delivery  if  erection  is  not  included,  and 
specify  by  whom  transportation  charges  are  to  be  paid. 

(d)  Give  requirements  as  to  working  drawings. 

Loads.  It  is  desirable  that  the  loads  used  in  making  the  design 
be  given  in  the  specifications  or  marked  on  the  drawings.  The 
latter  method  is  preferable  for  special  loads,  such  as  machinery, 
tanks,  storage  space,  etc.  This  information  is  needed  in  detailing 
connections,  stiffeners,  etc.  It  is  not  sufficient  to  say  that  con- 
nections shall  develop  the  full  strength  of  the  member,  for  there  may  • 
be  situations  when  a  concentrated  load  near  the  end  of  a  beam  may 
produce  a  stress  at  the  connection  greater  than  would  be  produced 
by  a  uniformly  distributed  load. 

Unit  Stresses.  The  unit  stresses  concern  the  design  of  the 
structural  steel  more  than  they  do  the  manufacture  and  construction 
of  it.  However,  they  are  needed  in  making  the  working  drawings 
and  should  be  included  in  the  specifications.  Those  given  in  Schnei- 


352  STEEL  CONSTRUCTION 

der's  Specifications  should  be  used  unless  local  building  ordinances 
require  other  values. 

Quality  of  Material.  The  quality -of  material  to  be  used  is  dis- 
cussed at  length  on  p.  42.  The  specifications  of  the  American 
Society  for  Testing  Materials  are  recommended  for  general  use. 
They  need  not  be  written  into  the  specifications,  it  being  sufficient 
to  state  that  the  steel  shall  comply  with  the  "Standard  Specifications 
for  Structural  Steel  for  Buildings",  adopted  by  the  American  Society 
for  Testing  Materials.  Similarly,  the  quality  of  cast  iron  may  be 
specified. 

In  this  section  the  kind  and  quality  of  paint  should  be  given. 

Details  of  Construction.  This  section  of  the  specifications  is 
concerned  with  such  items  as  connections,  rivet  spacing,  etc.  It  is 
chiefly  to  guide  the  engineers  and  draftsmen  in  making  working 
drawings.  Design  drawings  should  be  consistent  with  its  provisions. 

Schneider's  Specifications  are  recommended  for  this  portion  of 
the  specifications.  They  may  be  used  by  reference,  saying  that  the 
details  of  construction  should  conform  to  Schneider's  Specifications 
in  so  far  as  they  apply  to  this  work;  or  the  specific  paragraphs  which 
do  apply  may  be  referred  to  by  number. 

Workmanship.  The  specifications  for  workmanship  govern  the 
operations  in  the  shop.  Schneider's  Specifications  are  recom- 
mended and  may  be  used  the  same  as  for  construction  details. 

Painting.  This  is  well  covered  by  Schneider's  Specifications, 
which  may  be  used  without  modification  unless  some  special  pro- 
vision is  to  be  inserted. 

Inspection  and  Tests.  Schneider's  Specifications  are  used  for 
this  part  of  the  work  without  change. 

Erection.  The  specifications  for  erection  must  deal  with  the 
specific  job.  However,  some  of  its  provisions  are  general. 

The  conditions  at  the  site,  the  relations  to  the  other  parts  of  the 
structure,  order  of  procedure,  storage  available,  etc.,  etc.,  must  be 
written  to  suit  each  case.  If  the  contract  for  erection  is  separate 
from  the  contract  for  furnishing  the  steel,  the  division  between 
them  must  be  clearly  defined.  This  division  is  usually  best  made 
at  the  place  where  the  material  is  delivered  on  board  cars. 

Quality  of  workmanship  of  erection  applies  generally  to  all 
structures. 


STEEL  CONSTRUCTION  353 

EXAMPLE  OF  SPECIFICATIONS 

The  following  specifications  accord  with  the  preceding  discus- 
sions and  may  be  used  as  a  guide  in  writing  specifications  for  a  par- 
ticular structure. 

SPECIFICATIONS 

for  the 
Structural  Steel  and  Iron 

for  a 
(Kind  of  Building) 

for 
(Owner) 

Instructions  to  Bidders.  Bids  will  be  received  for  the  struc- 
tural steel  and  iron  work  required  for  (kind  of  building)  located  at 

Street,  in  the  City  of 

for  the  (°wner) 

in  accordance  with  the  following  specifications  and  the  plans  des- 
cribed therein. 

Bids  must  be  filed  at  the  office  of 

Architect,  on  or  before  noon, 19 

Bidders  shall  state  a  lump  sum  which  shall  include  furnishing, 
delivering,  and  erecting  the  structural  steel  and  iron  work  and  shall 
also  include  the  cost  pf  the  bond,  insurance,  and  watch  service  as 
required  under  general  conditions. 

General  Conditions. 

Ownership.  The  building  is  known  as  the Build- 
ing and  is  owned  by  the [a  partnership  (or 

corporation)  existing  under  the  laws  of  the  State  of ] 

Location.  It  is  located  at , 

Street  in  the  City  of on  lots (give 

legal  description). 

Bond.  The  contractor  shall  furnish  surety  bond  in  the  penal 
sum  of  one-half  the  contract  price,  guaranteeing  the  fulfillment  of 


354  STEEL  CONSTRUCTION 

the  terms  of  the  contract.  Said  bond  shall  be  in  terms  and  with 
surety  satisfactory  to  the  Architect. 

Liability  Insurance.  The  contractor  shall  protect  the  owner 
against  loss  due  to  any  damage  to  property  or  injury  to  persons 
which  may  result  from  his  operations.  He  shall  provide  adequate 
liability  insurance  in  a  company  approved  by  the  Architect. 

Patented  Articles.  The  contractor  shall  protect  the  owner 
against  any  claim  arising  out  of  the  use  of  any  patented  article, 
appliance,  or  method. 

Protection.  The  contractor  shall  provide  such  barricades, 
scaffolding,  staging,  and  other  means  of  protection  as  may  be  re- 
quired to  comply  with  the  state  and  municipal  laws  and  to  ade- 
quately safeguard  property  and  persons. 

Watchmen.  The  contractor  shall  keep  competent  watchmen  on 
the  building  day  and  night. 

Scope.  [Give  a  general  description  similar  to  the  following: 
The  building  is  designed  for  office  purposes  with  stores  on  the  first 
and  second  floors.  It  is  twenty  stories  high  above  street  level  with 
a  basement  and  sub-basement  below  street  level.  The  ground  area 
occupied  is  approximately  100  feet  by  162  feet.] 

Work  Covered.  The  work  to  be  done  under  the  specifications  is 
the  furnishing  and  the  erecting  of  the  structural  steel  and  iron  work. 
The  contractor  shall  make  the  working  drawings,  furnish  and  fabri- 
cate the  material,  pay  all  transportation  charges,  assemble  the 
material  in  place  in  the  building,  rivet  the  connections,  and  furnish 
the  materials  and  labor  for  shop  and  field  painting. 

Materials  Included.  The  structural  steel  and  iron  work 
consists  of  the  following  items:  (To  be  changed  to  suit  the 
case). 

Grillage  Beams  and  Girders 

Cast-Iron  Pedestals 

I-Beam  Reinforcement  in  Retaining  Walls 

Structural  Steel  Framework 

Cast-Iron  Columns 

Detached  Lintels 

Cornice  Brackets 

Roofing  Tees 

Steel  Chimney 

All  minor  parts  belonging  to  the  above  items 


STEEL  CONSTRUCTION  355 

It  includes  all  the  material  of  the  above  character  shown  in  the 
structural  plans  of  the  building  and,  in  addition,  it  includes  the 
detached  lintels  over  exterior  windows  which  are  shown  on  the 
architectural  plans. 

Materials  Not  Included.  The  structural  steel  and  iron  work 
(to  be  changed  to  suit  the  case)  does  not  include  the  angles,  channels, 
and  hangers  of  the  suspended  ceiling  over  the  top  story,  the  elevator 
sheave  beams,  the  beams  and  channels  for  the  stairs  other  than  those 
shown  on  the  framing  plans,  the  marquise  framing,  the  steel  column 
guards  and  door  guards  in  the  shipping  room,  and  other  like  items 
shown  on  the  architectural  plans.  It  does  not  include  the  rods  for 
reinforced  concrete  work  shown  on  the  structural  plans  except  cer- 
tain items  which  are  definitely  marked  on  the  drawings  to  be  fur- 
nished with  the  structural  steel. 

Plans.     The  structural  plans  consist  of  drawings  prepared  by 

Structural   Engineer  for 

Architect,  as  follows: 

(Give  list  of  drawings) 


The  architectural  plans  prepared  by 

Architect,  which  show  structural  steel  and  iron  work  not  given  on 
the  structural  plans  are  drawings  Xo 

While  making  the  working  drawings,  the  contractor  shall  con- 
sult all  architectural  drawings  which  may  be  supplied  to  him,  for 
the  purpose  of  discovering  discrepancies,  making  necessary  allow- 
ances for  clearance,  providing  connections  and  supports  for  other 
materials,  etc. 

\Yhen  provision  must  be  made  for  attaching  other  materials  to 
the  structural  steel  work,  the  contractor  shall  furnish  the  holes 
required.  If  the  necessary  data  are  not  given  on  the  structural  or 
architectural  drawings,  he  shall  apply  to  the  Architect  for  the  data 
before  completing  the  working  drawings.  This  applies  particularly 
to  stone,  terra  cotta,  concrete,  miscellaneous  iron,  ornamental  iron, 
furring  (wood  and  steel),  pipes,  and  conduits. 

Working  Drawings.  The  contractor  is  required  to  prepare 
working  drawings  to  supplement  the  'design  drawings  prepared  by 
the  Engineer  and  the  Architect.  Two  copies  of  such  drawings  shall 


356  STEEL  CONSTRUCTION 

be  submitted  to  the  Architect  for  approval.  After  approval,  three 
copies  shall  be  furnished  to  the  Architect  for  his  files,  and  as  many 
copies  as  may  be  required  shall  be  furnished  to  the  inspector  and  to 
other  trades. 

Copies  or  prints  of  drawings  issued  before  approval  shall  be 
marked  "Not  Approved"  and  those  issued  after  approval  shall  be 
marked  "Approved  Drawing."  During  the  preparation  of  the 
working  drawings,  the  contractor  shall  examine  the  design  drawings 
carefully  for  omissions  and  errors,  and  wrhen  such  omissions  and 
errors  are  discovered,  he  shall  submit  them  to  the  Architect  for 
correction.  Figured  dimensions  only  shall  be  used. 

If  the  contractor  does  not  have  a  force  of  engineers  competent 
to  prepare  working  drawings  to  the  satisfaction  of  the  Architect,  he 
shall  employ  a  consulting  engineer  for  that  purpose. 

Working  drawings  shall  be  accompanied  by  erection  diagrams 
and  a  complete  index  giving  marking  numbers  of  the  material  and 
page  or  sheet  numbers  of  the  drawings. 

Approval  of  Working  Drawings.  If  the  working  drawings  are 
found  to  be  consistent  with  the  design  drawings  and  these  specifica- 
tions, and  if  the  details  shown  on  them  are  satisfactory,  they  will  be 
approved.  One  copy  so  marked  will  be  returned  to  the  contractor. 
If  not  consistent  and  satisfactory  as  above,  one  copy  will  be  marked 
to  indicate  the  required  changes  and  returned  to  the  contractor^ 
who  shall  then  make  the  .required  changes,  and  if  so  ordered,  shall 
submit  copies  of  revised  drawings  for  final  approval. 

The  Architect's  approval  will  cover  the  arrangement  of  the 
principal  members  and  auxiliary  members,  and  the  strength  of  con- 
nections. At  the  same  time  an  effort  \vill  be  made  to  discover  any 
errors  in  sizes  of  material,  in  general  dimensions,  and  in  detail  dimen- 
sions; but  the  responsibility  for  these  items  shall  remain  with  the 
contractor. 

The  manufacturing  of  any  material  or  the  performing  of  any 
work  before  approval  of  working  drawings  will  be  entirely  at  the 
risk  of  the  contractor. 

Transportation.  The  contractor  shall  pay  all  costs  of  transpor- 
tation of  material  from  his  shop  to  the  building  site  and  shall  assume 
all  risk  of  loss  and  damage  in  transit. 

Loads.    The  structural  steel  and  iron  work  is  designed  to  sup- 


STEEL  CONSTRUCTION  357 

port  the  estimated  dead  loads  and  the  assumed  live  loads.  In 
making  the  working  drawings,  the  contractor  shall  design  all  con- 
nections to  carry  the  same  loads. 

The  dead  loads  are  the  actual  weights  of  all  materials  of  con- 
struction in  the  positions  which  they  occupy,  except  that  the  effect 
of  movable  partitions  may  be  assumed  to  be  equivalent  to  a  uni- 
formly distributed  load  of  25  pounds  per  square  foot  of  floor  on  all 
office  floors.  On  other  floors  and  along  corridors,  the  partitions 
shall  be  provided  for  where  they  occur. 

The  live  loads  for  which  this  structure  is  designed  are: 

(Subject  to  change) 


Roof 
Office  floor 
Second  floor 
First  floor 
Sidewalk 
Wagon  space  and 
snipping  room 

50  Ib.  per  sq.  ft. 
50  Ib.  per  sq.  ft. 
100  Ib.  per  sq.  ft. 
1251b.  per  sq.  ft. 
150  Ib.  per  sq.  ft. 

250  Ib.  per  sq.  ft. 

The  special  loads  from  elevators,  tanks,  etc.,  are  marked  on  the 
drawings. 

The  framework  is  designed  for  a  wind  pressure  of  20  pounds  per 
square  foot  applied  horizontally  to  the  vertical  projection  of  the 
building  in  any  direction. 

Where  stresses  are  marked  on  the  drawings,  they  may  be  used 
as  the  full  effect  of  the  loads. 

Beams  and  girders  shall  have  their  connections  made  strong 
enough  to  develop  the  full  capacity  of  the  members  when  they  are 
uniformly  loaded,  even  when  the  live  and  dead  loads  are  less  than 
this  capacity. 

Unit  Stresses.  The  design  is  based  on  the  unit  stresses  given 
in  Schneider's  Specifications,  *  paragraphs  19  to  34  inclusive.  These 
unit  stresses  shall  be  used  in  proportioning  the  details. 

Steel 

19.  Permissible  Strains.  All  parts  of  the  structure  shall  be  proportioned 
so  that  the  sum  of  the  dead  and  live  loads,  together  with  the  impact,  if  any, 
shall  not  cause  the  strains  to  exceed  those  given  in  the  following  table: 


*"Rcvi3cd  Specifications  for  Structural  Work  for  Buildings"  by  C.  C.  Schneider,  M.  Am. 
Soc.  C.  E.,  Trant.  Am.  Sec.  C.  E.,  Vol.  LIV,  Page  494. 


358  STEEL  CONSTRUCTION 

Pounds  per 
square  inch 

Tension,  net  section 16,000 

Direct  compression 16,000 

Shear,  on  rivets  and  pins 12,000 

Shear,  on  bolts  and  field  rivets 9,000 

Shear,  on  ^late-girder  web  (gross  section) 10,000 

Bearing  pressure,  on  pins  and  rivets 24,000 

Bearing  pressure,  on  bolts  and  field  rivets 18,000 

Fiber  strain,  on  pins 24,000 

20.  Permissible  Compression  Strains.  For  compression  members,  the 
permissible  strain  of  16,000  Ib.  per  sq.  in.  shall  be  reduced  by  the  following 
formula: 

p  =  16,000-70^ 

Where  p  =  permissible  working  strain  per  square  inch  in  compression; 

I  =  length  of  piece,  in  inches,  from  center  to  center  of  connections; 
r  =  least  radius  of  gyration  of  the  section,  in  inches. 

21  For  wind  bracing,  and  the  combined  strains  due  to  wind  and  the 
other  loading,  the  permissible  working  strains  may  be  increased  25%,  or  to 
20,000  Ib.  for  direct  compression  or  tension. 

22.  Provision  for  Eccentric  Loading.     In  proportioning  columns,  provision 
must  be  made  for  eccentric  loading. 

23.  Expansion  Rollers.     The  pressure  per  linear  inch  on  expansion  rollers 
shall  not  exceed  600  d,  where  d  =  diameter  of  rollers,  in  inches. 

24.  Combined  Strains.  Members  subject  to  the  action  of  both  axial  and 
bending  strains  shall  be  proportioned  so  that  the  greatest  fiber  strain  will  not 
exceed  the  allowed  limits  for  the  axial  tension  or  compression  in  that  member. 

25.  Reversal  of  Strains.     Members  subject  to  reversal  of  strains  shall  be 
proportioned  for  the  strain  giving  the  largest  section,  but  their  connections  shall 
be  proportioned  for  the  sum  of  the  strains. 

26.  Net  Sections.     Net  sections  must  be  used  in  calculating  tension  mem- 
bers, and  in  deducting  the  rivet  holes;  they  must  be  taken  |  in.  larger  than  the 
nominal  size  of  the  rivets. 

27  Pin-connected  riveted  tension  members  shall  have  a  net  section 
through  the  pin  holes  25%  in  excess  of  the  net  section  of  the  body  of  the  member. 
The  net  section  back  of  the  pin  hole  shall  be  at  least  0.75  of  the  net  section  through 
the  pin  hole. 

28.  Compression    Members    Limiting   Length.     No    compression    member 
shall  have  a  length  exceeding  125  times  its  least  radius  of  gyration,  except  those 
for  wind  and  lateral  bracing,  which  may  have  a  length  not  exceeding  150  times 
the  least  radius  of  gyration. 

29.  Plate  Girders.     Plate  girders  shall  be  proportioned  on  the  assumption 
that  one-eighth  of  the  gross  area  of  the  web  is  available  'as  flange  area.     The 
compression  flange  shall  have  at  least  the  same  sectional  area  as  the  tension 
flange,  but  the  unsupported  length  of  the  flange  shall  not  exceed  16  times  its  width. 

30.  In  plate  girders  used  as  crane  runways,  if  the  unsupported  length  of 
the  compression  flange  exceeds  12  times  its  width,  the  flange  shall  be  figured  as 
a  column  between  the  points  of  support. 


STEEL  CONSTRUCTION  359 

51.  Web  Stiff eriers.    The  web  shall  have  stiffeners  at  the  ends  and  inner 
edges  of  bearing  plates,  and  at  all  points  of  concentrated  loads,  and  also  at 
intermediate  points,  when  the  thickness  of  the  web  is  less  than  one-sixtieth  of 
the  unsupported  distance  between  flange  angles,  generally  not  farther  apart  than 
the  depth  of  the  full  web  plate,  with  a  minimum  limit  of  5  feet. 

52.  Rotted  Beams.    I-beams,  and  channels  used  as  beams  or  girders,  shall 
be  proportioned  by  their  moments  of  inertia. 

53.  Limiting  Depth  of  Beams  and  Girders.    The  depth  of  rolled  beams  in 
floors  shall  be  not  less  than  one-twentieth  of  the  span  and,  if  used  as  roof  purlins, 
not  less  than  one-thirtieth  of  the  span. 

In  case  of  floors  subject  to  shocks  and  vibrations,  the  depth  of  beams  and 
girders  shall  be  limited  to  one-fifteenth  of  the  span.  If  shallower  beams  are 
used,  the  sectional  area  shall  be  increased  until  the  maximum  deflection  is  not 
greater  than  that  of  a  beam  having  a  depth  of  one-fifteenth  of  the  span,  but  the 
depth  of  such  beams  shall  in  no  case  be  less  than  one-twentieth  of  the  span. 
Cast  Iron 

$4>    Permissible  Strains.    Compression 12,000  Ib.  per  sq.  in. 

Tension 2,500  "      w     "    " 

Shear , 1,500  "     "     "    " 

Quality  of  Materials.  Steel.  The  structural  steel  shapes, 
plates,  and  rivets  shall  conform  to  the  Standard  Specifications  for 
Structural  Steel  for  Buildings  adopted  by  tho  American  Society  for 
Testing  Materials*,  as  follows; 

SPECIFICATIONS  FOR  STRUCTURAL  STEEL  FOR  BUILDINGS 

Structural  steel  may  be  made  by  either  the  open-hearth  or  Bessemer 
process. 

Rivet  steel  and  plate  or  angle  material  over  f  inch  thick,  which  is  to  be 
punched,  shall  be  made  by  the  open-hearth  process.. 

The  chemical  and  physical  properties  shall  conform  to  the  limits  shown  in 
the  tabular  matter  on  the  following  page. 

For  the  purposes  of  these  specifications,  the  yield  point  shall  be  determined 
by  the  careful  observation  of  the  drop  of  the  beam  or  halt  in  the  gage  of  the 
testing  machine. 

In  order  to  determine  if  the  material  conforms  to  the  chemical  limitations 
prescribed  *  *  *  *  *  *  *  •  analysis  shall  be  made  by  the  manufacturer 
from  a  test  ingot  taken  at  the  time  of  the  pouring  of  each  melt. or  blow  of  steel, 
and  a  correct  copy  of  such  analysis  furnished  to  the  engineer  or  his  inspector. 

Specimens  for  tensile  and  bending  tests  shall  be  made  by  cutting  coupons 
from  the  finished  product,  which  shall  have  both  faces  rolled  and  both  edges 
milled  to  the  form  shown  by  Fig.  1  (see  Fig.  46);  or  with  both  edges  parallel;  or 
they  may  be  turned  to  a  diameter  of  f  inch  for  a  length  of  at  least  9  inches, 
with  enlarged  ends. 

(a)  For  material  more  than  f  inch  thick  the  bending  test  specimen  may  be 
1  inch  by  \  inch  in  section. 

(6)     Rivet  rounds  and  small  rolled  bars  shall  be  tested  as  rolled. 

•American  Society  for  Testing  Materials,  Edgar  Marburg,  Secretary,  University  of  Penn- 
•ylvania,  Philadelphia. 


360 


STEEL  CONSTRUCTION 
Properties  of  Structural  Steel 


Properties  Considered 

Structural  Steel 

Rivet  Steel,  Open 
Hearth 

Phosphorus,  max.,  Bessemer.  .....,.,.. 

0.10  per  cent 

Phosphorus,  max.,  open  hearth  

0.06  per  cent 

0  06  per  cent 

Ult.  tensile  strength,  pounds  per  sq.  in.  . 

55,000-05,000 
i  Ult.  tens  str 

48,000-58,000 
i  Ult  tens  str 

Elongation,  min.  per  cent  in  8  in.  *...... 

1,400.000 

1,400,000 

Ult.  tens.  str. 
Silky 

Ult.  tens.  str. 
Silky 

180°  to  diameter 

180°  flat 

of  1  thickness 

Material  which  is  to  be  used  without  annealing  or  further  treatment  shall 
be  tested  in  the  condition  in  which  it  comes  from  the  rolls.  When  material  is  to 
be  annealed  or  otherwise  treated  before  use,  the  specimens  for  tensile  tests, 
representing  such  material,  shall  be  cut  from  properly  annealed  or  similarly 
treated  short  lengths  of  the  full  section  of  the  bar. 

At  least  one  tensile  and  one  bending  test  shall  be  made  from  each  melt  or 
blow  of  steel  as  rolled.  In  case  steel  differing  f  inch  and  more  in  thickness  is 
rolled  from  one  melt  or  blow,  a  test  shall  be  made  from  the  thickest  and  thinnest 
material  rolled.  ,  Should  either  of  these  test  specimens  develop  flaws,  .or  should 
the  tensile  test  specimen  break,  outside  of  the  middle  third  of  its  gaged  length, 
it  may  be  discarded  and  another, test  specimen  substituted  therefor.  If  tensile 
test  specimen  does  not  meet  the  specification,  additional  tests  may  be  made. 

(c)  The  bending  test  may  bo  made  by  pressure  or  by  blows. 

For  material  less  than  &  inch  and  more  than  f  inch  in  thickness,  the  follow- 
ing modifications  shall  be  made  in  the  requirements  for  elongation. 

(d)  For  each  increase  of  i  inch  in  thickness  above  f  inch,  a  deduction  of 
1  shall  be  made  from  the  specified  percentage  of  elongation. 

(e)  For  each  decrease  of  ^  inch  in  thickness  below  •&  inch,  a  deduction 
of  1\  shall  be  made  from  the  specified  percentage  of  elongation. 

(/)  For  pins,  the  required  percentage  of  elongation  shall  be  5  less  than 
that  specified  *****  as  determined  on  a  test  specimen,  the  center  of 
which  shall  be  1  inch  from  the  surface. 

Finished  material  must  be  free  from  injurious  seams,  flaws,  or  cracks,  and 
have  a  workmanlike  finish. 

Test  specimens  and  every  finished  piece  of  steel  shall  be  stamped  with  melt 
or  blow  number,  except  that  small  pieces  may  be  shipped  in  bundles  securely 
wired  together,  with  the  melt  or  blow  number  on  a  metal  tag  attached- 

A  variation  in  cross  section  or  weight  of  each  piece  of  steel  of  more  than  2f 
per  cent  from  that  specified  will  be  sufficient  cause  for  rejection,  except  in  case 
of  sheared  plates,  which  will  be  covered  by  the  following  permissible  variations, 
which  are  to  apply  to  single  plates. 


STEEL  CONSTRUCTION' 


361 


When  Ordered  to  Weight 

Plates  12\  pounds  per  square  foot  or  heavier: 

(g)     Up  to  100  inches  wide,  2^  per  cent  above  or  below  the  prescribed 

weight. 

(h)     100  inches  wide  and  over,  5  per  cent  above  or  below. 
Plates  under  i2\  pounds  per  square  foot: 

(£)      Up  to  75  inches  wide,  2\  per  cent  above  or  below. 

75  inches  and  up  to  100  inches  wide,  5  per  cent  above  or  3  per  cent 

below. 
0)      100  inches  wide  and  over,  10  per  cent  above  or  3  per  cent  below. 

When  Ordered  to  Gage 

Plates  will  be  accepted  if  they  measure  not  more  than  0.01  inch  below  the 
ordered  thickness. 

An  excess  over  the  nominal  weight  corresponding  to  the  dimensions  on  the 
order  will  be  allowed  for  each  plate,  if  not  more  than  that  shown  in  the  following 
tables,  one  cubic  inch  of  rolled  steel  being  assumed  to  weigh  0.2833  pound. 

Plates  \  inch  and  over  in  thickness 


Thickness 
Ordered. 
Inches 

Nominal 
Weights 
Lb.  per 
sq.  ft. 

Width  of  Plate 

Up  to  75  in. 

75  in.  and  up 
to  100  in. 

100  in.  and 
up  to  115  in. 

Over  115  in. 

1-4 
5-16 
3-8 
7-16 
1-2 
9-16 
5-8 
Over  5-8 

10.20 
12.75 
15.30 
17  85 
20.40 
22.95 
25.50 

10  per  cent 
8  per  cent 
7  per  cent 
6  per  cent 
5  per  cent 
4|  per  cent 
4  per  cent 
3  1  per  cent 

14  per  cent 
12  per  cent 
10  per  cent 
8  per  cent 
7  per  cent 
6|  per  cent 
6  per  cent 
5  per  cent 

18  per  cent 
16  per  cent 
13  per  cent 
10  per  cent. 
9  per  cent 
8|  per  cent 
.    8  per  cent 
6£  per  cent 

17  per  cent 
13  per  cent 
12  per  cent 
1  1  per  cent 
10  per  cent 
9  per  cent 

Plates  under  \  inch  in  thickness 


Thickness 
Ordered 
Inches 

Nominal 
Weights 
Lb.  per  sq.  ft. 

Width  of  Plate 

Up  to  50  in. 

50  in.  and  up 
to  70  in. 

Over  70  in. 

1-8    up  to  5-32 
5-32  up  to  3-16 
3-16  up  to  1-4 

5.10  to    6.37 
6.37  to    7.65 
7.65  to  10.20 

10    per  cent 
8^  per  cent 
7    per  cent 

15    per  cent 
12|  per  cent 
10    per  cent 

20  per  cent 
17  per  cent 
15  per  -cent 

The  inspector  representing  the  purchaser  shall  have  all  reasonable  facilities 
afforded  to  him  by  the  manufacturer  to  safisfy  him  that  the  finished  material  is 
furnished  in  accordance  with  these  specifications. 

All  tests  and  inspections  shall  be  made  at  the  place  of  manufacture,  prior 
to  shipment. 

Cast  Iron.  The  cast  iron  shall  conform  to  the  Standard  Speci- 
fications for  Gray  Iron  Castings  adopted  by  the  American  Society 
for  Testing  Materials*,  as  follows: 

*American  Society  for  Testing  Materials,  Edgar  Marburg,  Secretary,  University  of  Penn- 
sylvania, Philadelphia. 


362  STEEL  CONSTRUCTION 

SPECIFICATIONS   FOR  GRAY   IRON   CASTINGS 

Unless  furnace  iron  is  specified,  all  gray  castings  are  understood  to  be 
made  by  the  cupola  process. 

The  sulphur  contents  to  be  as  follows: 

Light  castings ,....".*...  .not  over  0.08  per  cent 

Medium  castings not  over  0.10  per  cent 

Heavy  casting not  over  0.12  per  cent 

In  dividing  castings  into  light,  medium,  and  heavy  classes,  the  following 
standards  have  been  adopted:. 

Castings  having  any  section  less  than  Hnch  thick  shall  be  known  as  light 
castings. 

Castings  in  which  no  section  is  less  than  2  inches  thick  shall  be  known  as 
heavy  castings. 

Medium  castings  are  those  not  included  in  the  above  classification. 

Transverse  Test.  The  minimum  breaking  strength  of  the  "Arbitration  Bar" 
under  transverse  load  shall  not  be  under: 

Light  castings . . . . i.. ..... .2,500  lb. 

Medium  castings 2,900  lb. 

Heavy  castings. ................ , .  .3,300  lb. 

In  no  case  shall  the  deflection  be  under  0.10  inch. 

Tensile. Test.    Where  specified,  this  shall  not  run  less  than; 

Light  castings , 18,000  lb.  per  'sq.  in. 

Medium  castings 21,000  lb.  per  sq.  in. 

Heavy  castings 24,000  lb.  per  sq.  in. 

The  quality  of  the  iron  going  into  castings  under  specification  shall  be 
determined  by  means  of  the  "Arbitration  Bar".  •  This.is  a  bar  1 J  inches  in  diam- 
eter and  15  inches  long.  It  shall  be  prepared  as  stated  further  on  and  tested 
transversely.  The  tensile  test  is  not  recommended,  but  in  case  it  is  called  for, 
the  bar  as  shown  in  Fig.  1,  (figure  not  given)  and  turned  up  from  any  of  the 
broken  pieces  of  the  transverse  test  shall  be  used.  The  expense  of  the  tensile 
test  shall  fall  on  the  purchaser. 

Two  sets  of  two  bars  shall  be  cast  from  each  heat,  one  set  from  the  first 
and  the  other  set  from  the  last  iron  going  into  the  castings.  Where  the  heat 
exceeds  twenty  tons,  an  additional  set  of  two  bars  shall  be  cast  for  each  twenty 
tons  or  fraction  thereof  above  this  amount.  In  case  of  a  change  of  mixture 
during  the  heat,  one  set  of  two  bars  shall  also  be  cast  for  every  mixture 
other  than  the  regular  one.  Each  set  of  two  bars  is  to  go  into  a  single  mold. 
The  bars  shall  not  be  rumbled  or  otherwise  treated,  being  simply  brushed  of! 
before  testing. 

The  transverse  test  shall  be  made  on  all  the  bars  cast,  with  supports  12 
inches  apart,  load  applied  at  the  middle,  and  the  deflection  at  rupture  noted. 
One  bar  of  every  two  of  each  set  made  must  fulfil  the  requirements  to  permit 
acceptance  of  the  castings  represented. 

The  mold  for  the  bars  is  shown  in  Fig.  2  (figure  not  given.).  The  bottom 
of  the  bar  is  ^  inch  smaller  in  diameter  than  the  top,  to  allow  for  draft  and  for 
the  strain  of  pouring.  The  pattern  shall  not  be  rapped  before  withdrawing. 
The  flask  is  to  be  rammed  up  with  green  molding  sand,  a  little  damper  than 


STEEL  CONSTRUCTION  363 

usual,  well  mixed  and  put  through  a  No.  8  sieve,  with  a  mixture  of  one  to  twelve 
bituminous  facing  The  mold  shall  be  rammed  evenly  and  fairly  hard,  thor- 
oughly dried,  and  not  cast  until  it  is  cold.  The  test  bar  shall  not  be  removed 
from  the  mold  until  cold  enough  to  be  handled. 

The  rate  of  application  of  the  load  shall  be  from  20  to  40  seconds  for  a 
deflection  of  0.10  inch. 

Borings  from  the  broken  pieces  of  the  "Arbitration  Bar"  shall  be  used  for 
the  sulphur  determinations.  One  determination  for  each  mold  made  shall  be 
required.  In  case  of  dispute,  the  standards  of  the  American  Foundrymen's 
Association  shall  be  used  for  comparison. 

Castings  shall  be  true  to  pattern,  free  from  cracks,  flaws,  and  excessive 
shrinkage.  In  other  respects  they  shall  conform  to  whatever  points  may  be 
specially  agreed  upon. 

The  inspector  shall  have  reasonable  facilities  afforded  him  by  the  manu- 
facturer to  satisfy  him  that  the  finished  material  is  furnished  in  accordance  with 
these  specifications.  All  tests  and  inspections  shall,  as  far  as  possible,  be  made 
at  the  place  of  manufacture  prior  to  shipment. 

Paint.  The  paints  used  shall  be  red  lead  paint  for  the  shop 
coat  and  graphite  paint  for  the  field  coat. 

The  red  lead  paint  shall  be  made  of  red  lead  containing  not  less 
than  95  per  cent  Pb3  O4,  for  the  pigment  and  pure  raw  linseed  oil 
with  not  more  than  8  per  cent  of  turpentine  or  Japan  drier  for  the 
vehicle. 

The  red  lead  paint  shall  be  mixed  on  the  premises  where  it  is 
used,  and  each  batch  shall  be  used  within  twenty-four  hours  after 
being  mixed.  The  mixing  shall  be  done  in  a  churn  or  other 
mechanical  mixer.  The  material  shall  be  used  in  the  proportion 
of  twenty-five  pounds  of  red  lead  to  one  gallon  of  oil. 

The  contractor  shall  furnish -samples  of  the  lead  and  oil  for 
testing,  and  if  required  to  do  so  shall  furnish  the  name  of  the  manu- 
facturer of  the  oil  and  of  the  dealers  who  have  handled  it. 

The  graphite  shall  be  the 

brand  manufactured  by  the Company, 

or  any  other  graphite  paint  of  equal  quality,  if  it  is  approved  by  the 
Architect. 

The  contractor  shall  furnish  samples  of  the  graphite  paint  for 
analysis  and  test.  He  shall  guarantee  that  the  paint  will  fulfill  all 
the  published  claims  made  for  it  by  its  manufacturer. 

Details  of  Construction.  The  details  of  construction  shall  con- 
form to  paragraphs  37  to  81,  inclusive,  of  Schneider's  Specifications, 
in  so  far  as  their  provisions  are  applicable  to  this  work. 


364  .      STEEL  CONSTRUCTION 

37.  Minimum  Thickness  of  Material     No  steel  of  less  than  \  in.  thickness 
shall  be  used,  except  for  lining  or  filling  vacant  spaces. 

38.  Adjustable  Members.    Adjustable  members  in  any  part  of  structures 
shall  preferably  be  avoided. 

39.  Symmetrical  Sections.    Sections  shall  preferably  be  made  symmetrical. 

40.  Connections.    The    strength    of    connections    shall    be    sufficient    to 
develop  the  full  strength  'of  the  member: 

41.  No  connection,  except  lattice  bars,  shall  have  less  than  two  rivets. 

42.  Floor  Beams.     Floor  beams  "shall  generally  be  rolled  steel  beams. 

43.  For  fireproof  floors,  they  shall  generally  be  tied  with  tie-rods  at  inter- 
vals not  exceeding  eight  times  the  depth  of  the  beams.     This  spacing  may  be 
increased  for  floors  which  are  not  of  the  arch  type  of  construction.     Holes  for 
tie-rods,  where  the  construction  of  the  floor  permits,  shall  be  spaced  about  3  in. 
above  the  bottom  of  the  beam. 

44-  Beam  Girder.-  When  more  than  one  rolled  beam  is  used  to  form  a 
girder,  they  shall  be  connected  by  bolts  and  separators  at  intervals  of  not  more 
than  5  ft.  All  beams  having  a  depth  of  12  in.  and  more  shall  have  at  least  two 
bolts  to  each  separator. 

45.  Wall  Ends  of  Beams  and.  Girders.    Wall  ends  of  a  sufficient  number 
of  joists  and  girders  shall  be  anchored  securely  to  impart  rigidity  to  the  structure. 

46.  Wall  Plates  and  Column  Bases.     Wall  plates  and  column  bases  shall 
be  constructed  so  that  the  load  will  be  well  distributed  over  the  entire  bearing. 
If  they  do  not  get  the  full  bearing  on  the  masonry,  the  deficiency  shall  be  made 
good  with.Portland  cement  mortar. 

'47.  Floor  Girders.  The  floor  girders  may  be  rolled  beams  or  plate  girders ; 
they  shall  preferably  be  'riveted  or  bolted  to  columns  by  means  of  connection 
angles.  Shelf  angles  or  other  support  may  be  provided  for  convenience  during 
erection. 

48.  Flange  Plates.    The  flange  plates  of  all  girders  shall  be  limited  in  width, 
so  as  not  to  extend,  beyond  the  outer  line  of  rivets  connecting  them  to  the  angles, 
more  than  6  in.,  or  more  than  eight  times  the  thickness  of  the  thinnest  plate. 

49.  Web  Stiffeners.    Web  stiffeners'  shall  be  in  pairs,  and  shall  have  a  close 
bearing  against  the  flange  angles.     Those  over  the  end  bearing,  or  forming  the 
connection  between  girder  and  column,  shall  be  on  fillers'.     Intermediate  stiff- 
eners may  be  on  fillers  or  crimped  over  the  flange  angles.    The  rivet  pitch  in 
stiffeners  shall  not  be  more  than  5  in. 

50.  Web  Splices.    Web  plates  of  girders  must  be  spliced  at  all  points  by 
a  plate  on  each  side  of  the  web,  capable  of  transmitting  the  full  strain  through 
splice  rivets. 

51.  Columns.    Columns  shall  be  designed  so  as  to  provide  for  effective 
connections  of  floor  beams,  girders,  or  brackets. 

They  shall  preferably  be  continuous  over  several  stories. 

52.  Column  Splices.    The  splices  shall  be  strong  enough  to  resist  the 
bending  strain  and  make  the  columns  practically  continuous  for  their  whole  length. 

53.  Trusses.    Trusses   shall    preferably    be   riveted    structures.    Heavy 
trusses  of  long  span,  where  the  riveted  field  connections    would  become  un- 
wieldy, or  for  other  good  reasons,  may  be  designed  as  pin-connected  structures. 

54.  Intersecting  Members.     Main  members  of  trusses  shall  be  designed  so 
that  the  neutral  axes  of  intersecting  members  shall  meet  in  a  common  point. 


STEEL  CONSTRUCTION  365 

55.  Roof  Trusses.  Roof  trusses  shall  be  braced  in  pairs  in  the  plane  of 
the  chords. 

Purlins  shall  be  made  of  shapes,  or  riveted-up  plate,  or  lattice  girders- 
Trussed  purlins  will  not  be  allowed. 

66.  Eyebars.    The  eyebars  in  pin-connected  trusses  composing  a  member 
shall  be  as  nearly  parallel  to  the  axis  of  the  truss  as  possible. 

67.  Spacing  of  Rivets.    The  minimum  distance  between  centers  of  rivet 
holes  shall  be  three  diameters  of  the  rivet;  but  the  distance  shall  preferably  be 
not  less  than. 3  in.  for  J-in.  rivets.  24  in.  for  l-in.  rivets,  2i  in.  for  f-in.  rivets, 
and  1J  in.  for  $-in.  rivets. 

68.  For  angles  with  two  gage  lines,  with  rivets  staggered,  the  maximum 
in  each  line  shall  be  twice  as  great  as  given  in  Paragraph  57,  and,  where  two  or 
more  plates  are  used  in  contact,  rivets  not  more  than  12  in.  apart  in  any  direc- 
tion shall  be  used  to  hold  the  plates  together. 

59.  The  pitch  of  the  rivet,  in  the  direction  of  the  strain,  shall  not  exceed 
6  in.,  nor  16  times  the  thinnest  outside  plate  connected,  and  not  more  than  50 
times  that  thickness  at  right  angles  to  the  strain. 

60.  Edge  Distance.    The  minimum  distance  from  the  center  of  any  rivet 
hole  to  a  sheared  edge  shall  be  1  j  in.  for  |-in.  rivets,  1  \  in.  for  f-in.  rivets,  \\  in. 
for  |-in.  rivets,  and  I  in.  for  £-in.  rivets;  and  to  a  rolled  edge,  11,  1J,  1,  and  fin., 
respectively. 

61.  The  maximum  distance  from  any  edge  shall  be  eight  times  the  thick- 
ness of  the  plate. 

62.  Maximum  Diameter.     The  diameter  of  the  rivets  in  any  angle  carrying 
calculated  strains  shall  not  exceed  one-quarter  of  the  width  of  the  leg  in  which 
they  are  driven.     In  minor  parts,  rivets  may  be  \  in.  greater  in  diameter. 

63.  Pitch  at  Ends.    The  pitch  of  rivets  at  the  ends  of  built  compression 
members  shall  not  exceed  four  diameters  of  the  rivets  for  a  length  equal  to  one 
and  one-half  times  the  maximum  width  of  the  member. 

64"  Tie  Plates.  The  open  sides  of  compression  members  shall  be  provided 
with  lattice  having  tie  plates  at  each  end  at  intermediate  points  where  the 
lattice  is  interrupted.  The  tie  plates  shall  be  as  near  the  ends  as  practicable. 
In  main  members,  carrying  calculated  strains,  the  end  tie  plates  shall  have  a 
length  not  less  than  the  distance  between  the  lines  of  rivets  connecting  them  to 
the  flanges,  and  intermediate  ones  not  less  than  half  this  distance. 

Their  thickness  shall  be  not  less  than  one-fiftieth  of  the  same  distance. 

65.  Lattice.    The  thickness  of  lattice  bars  shall  be  not  less  than  one-fortieth 
for  single  lattice  and  one-sixtieth  for  double  lattice,  of  the  distance  between  end 
rivets;  their  minimum  width  shall  be  as  follows: 

For  15-in.  channels,  or  built  sections \0,  •      n  •       •     .„  % 

with  3*  and  4-in.  angles ?*  m'  (i'ln*  nvets) 

For  12-,  10- and  9-in.  channels,  or  built  \01  •  /,  .  •  .  \ 

sections  with  3-in.  angles /2«  m"  (*-'n-  nvets) 

For  &•  and  7-in.  channels,  or  built  \0  -  ,5  :  .  .  ^ 

sections  with  2J-in.  angles J2  m'  (*'m'  nvets) 

For  6-  and  5-in.  channels,  or  built \ia  •  fl  •  ,  % 

sections  with  2-in.  angles I1*  ln'  (^In'  nvets) 

66.  Lattice  bars  with  two  rivets  shall  generally  be  used  in  flanges  more 
than  5  in.  wide. 


366  STEEL  CONSTRUCTION 

67.  Angle  of  Lattice.     The  inclination  of  lattice  bars  with  the  axis  of  the 
member,  generally,  shall  be  not  less  than  45°,  and  when  the  distance  between 
the  rivet  lines  in  the  flange  is  more  than  15  in.,  if  a  single  rivet  bar  is  used,  the 
lattice  shall  be  double  and  riveted  at  the  intersection. 

68.  Spacing  of  Lattice.     The  pitch  of  lattice  connections,  along  the  flange 
divided  by  the  least  radius  of  gyration  of  the  member  between  connections, 
shall  be  less  than  the  corresponding  ratio  of  the  member  as  a  whole. 

69.  Faced  Joints.    Abutting  joints  in  compression  members  when  faced 
for  bearing  shall  be  spliced  sufficiently  to  hold  the  connecting  members  accur- 
ately in  place. 

70.  All  other  joints  in  riveted  work,  whether  in  tension  or  compression, 
shall  be  fully  spliced 

71.  Pin  Plates.     Pin  holes  shall  be  reinforced  by  plates  where  necessary; 
and  at  least  one  plate  shall  be  as  wide  as  the  flange  will  allow;  where  angles  are 
used,  this  plate  shall  be  on  the  same  side  as  the  angles.     The  plates  shall  contain 
sufficient  rivets  to  distribute  their  portion  of  the  pin  pressure  to  the  full  cross 
section  of  the  member 

72.  Pins.     Pins  shall  be  long  enough  to  insure  a  full  bearing  of  all  parts 
connected  upon  the  turned-down  body  of  the  pin 

73.  Members  packed  on  pins  shall  be  held  against  lateral  movement. 

74.  Bolts.    Where  members  are  connected  by  bolts,  the  body  of  these 
bolts  shall  be  long  enough  to  extend  through  the  metal.     A  washer  at  least 
&  in  thick  shall  be  used  under  the  nut 

75.  Fillers.    Fillers  between  parts  carrying  strain  shall  have  a  sufficient 
number  of  independent  rivets  to  transmit  the  strain  to  the  member  to  which  the 
filler  is  attached 

76.  Temperature.     Provision  shall  be  made  for  expansion  and  contraction, 
corresponding  to  a  variation  of  temperature  of  150°  Fahr.,  where  necessary. 

77.  Rollers.     Expansion  rollers  shall  be  not  less  than  4  in.  in  diameter. 

78.  Stone  Bolts     Stone  bolts  shall  extend  not  less  than  4  in.  into  granite 
pedestals  and  8  in.  into  other  material. 

79.  Anchorage.     Columns  which  are  strained  in  tension  at  their  base  shall 
be  anchored  to  the  foundations 

80.  Anchor  bolts  shall  be  long  enough  to  engage  a  mass  of  masonry,  the 
weight  of  which  shall  be  one  and  one-half  times  the  tension  in  the  anchor 

81.  Bracing.     Lateral,  longitudinal,  and  transverse  bracing  in  all  struc- 
tures shall  preferably  be  composed  of  rigid  members. 

Adjacent  ends  of  column  sections,  which  do  not  have  full  bear- 
ing, shall  have  bearing  plates  not  less  than  f  inch  thick. 

Rivets  generally  shall  be  f  inch  in  diameter,  but  the  diameter  of 
the  rivet  shall  not  be  less  than  one-fourth  of  its  grip;  |-inch  rivets 
shall  be  used  when  the  pieces  connected  are  f  inch  or  more  in  thickness. 

No  beam  connections  shall  be  less  than  the  standards  of  the 
American  Bridge  Company. 

The  clearance  from  the  ends  of  beams  to  columns  or  to  girders 
shall  not  exceed  \  inch. 


STEEL  CONSTRUCTION  367 

Tie-rods  between  floor  beams  shall  be  threaded  at  both  ends  for 
a  length  of  at  least  3  inches. 

The  number  of  rivets  furnished  for  field  connections  shall  be 
10  per  cent  in  excess  of  the  nominal  number  required. 

Chimney.  The  connections  of  the  cast-iron  or  steel  chimney  to 
the  framework  shall  be  such  as  to  permit  expansion  and  contraction, 
due  to  changes  in  temperature. 

Provide   flanges  with   holes   for  breeching  connection. 

Cast-iron  chimneys  may  have  either  flanged  joints  or  hub  and 
spigot  joints.  The  bearing  surfaces  shall  have  contact  on  the  entire 
perimeter  and  shall  be  exactly  at  right  angles  to  the  axis  of  the  pipe, 
being  turned  or  planed,  if  necessary  to  make  them  so.  The  calking 
space  in  hub  and  spigot  joints  shall  be  filled  with  iron  fillings  and 
sal  ammoniac  and  calked  solid.  Connections  for  anchors  shall  be 
cast  on. 

Steel  chimneys  shall  have  lap  joints  for  all  shop  connections. 
They  may  have  either  lap  or  flange  joints  for  the  field  connections, 
except  that  the  lap  joints  generally  will  be  required  for  self-support- 
ing chimneys  exposed  to  wind  pressure.  All  joints  shall  be  prac- 
tically air-tight  and,  if  not  so  made  by  the  riveting,  shall  be  calked. 

Cast  Iron.  The  ends  of  cast-iron  columns  and  the  tops  of  cast- 
iron  base  plates  and  pedestals  shall  be  planed. 

Bolt  holes  in  cast  iron  shall  be  drilled.  Holes  for  grout  may  be 
cored. 

In  each  cast-iron  pedestal  a  grout  hole  shall  be  provided  which 
shall  be  not  less  than  2|  inches  in  diameter  and  placed  as  near  the 
center  of  the  base  as  practicable.  Additional  holes  shall  be  provided 
in  bases  larger  than  4  feet  in  diameter. 

The  joints  in  cast-iron  columns  shall  be  made  by  means  of 
flanges  cast  on  the  columns.  Each  joint  shall  be  bolted  with  not 
less  than  four  J-inch  bolts.  The  metal  in  the  flanges  shall  be  not  less 
than  1  inch  thick. 

Unless  otherwise  designed,  each  beam  connection  shall  consist 
of  a  bracket  and  a  lug.  The  bracket  shall  sustain  the  entire  reaction 
from  the  beam.  It  shall  project  not  less  than  4  inches  from  the 
column  and  shall  slope  J  inch.  The  lug  shall  provide  for  two  or 
more  bolts  connecting  to  the  web  of  the  beam. 


368  STEEL  CONSTRUCTION 

Workmanship.  The  workmanship  in  the  fabrication  of  the 
structural  steel  shall  conform  to  paragraphs  23  to  51  of  Schneider's 
Specifications,  in  so  far  as  they  concern  this  work. 

23  General.  All  parts  forming  a  structure  shall  be  built  in  accordance 
with  approved  drawings  The  workmanship  and  finish  shall  be  equal  to  the 
best  practice  in  modern  bridge  work. 

S4.  Straightening  Material  Material  shall  be  thoroughly  straightened  in 
the  shop,  by  methods  which  will  not  injure  it,  before  being  laid  off  or  worked  in 
any  way. 

25.  Finish.     Shearing  shall  be  done  neatly  and  accurately,  and  all  por- 
tions of  the  work  exposed  to  view  shall  be  neatly  finished 

26.  Rivets.     The  size  of  rivets  called  for  on  the  plans  shall  be  understood 
to  mean  the  actual  size  of  the  cold  rivet  before  heating. 

27.  Rivet  Holes.    The  diameter  of  the  punch  for  material  not  more  than 
|  in.  thick  shall  be  not  more  than  pg  in.,  nor  that  of  the  die  more  than  |  in.  larger 
than  the  diameter  of  the  rivet.     Material  more  than  |  in    thick,  excepting  in 
minor  details,  shall  be  sub-punched  and  reamed  or  drilled  from  the  solid 

28.  Punching.     Punching  shall  be  done  accurately.     Slight  inaccuracy  in 
the  matching  of  holes  may  be  corrected  with  reamers.     Drifting  to  enlarge 
unfair  holes  will  not  be  allowed.     Poor  matching  of  holes  will  be  cause  for  rejec- 
tion, at  the  option  of  the  inspector 

29.  Assembling.     Riveted  members  shall  have  all  parts  well  pinned  up 
and  firmly  drawn  together  with  bolts  before  riveting  is  commenced.     Contact 
surfaces  shall  be  painted      (See  Paragraph  52.) 

30.  Lattice  Bars.     Lattice  bars  shall  have   neatly-rounded  ends,  unless 
otherwise  called  for. 

31.  Web  Stiff eners.     Stiffeners  shall   fit  neatly   between   the   flanges  of 
girders.    Where  tight  fits  are  called  for,  the  ends  of  the  stiffeners  shall  be  faced 
and  shall  be  brought  to  a  true  contact  bearing  with  the  flange  angles 

32.  Splice  Plates  and  Fillers.     Web  splice  plates  and  fillers  under  stiffeners 
shall  be  cut  to  fit  within  f  in.  of  flange  angles. 

33  Connection  Angles.  Connection  angles  for  floor  girders  shall  be  flush 
with  each  other  and  correct  as  to  position  and  length  of  girder. 

34'  Riveting.  Rivets  shall  be  driven  by  pressure  tools  wherever  possible. 
Pneumatic  hammers  shall  be  used  in  preference  to  hand  driving 

35  Rivets.  Rivets  shall  look  neat  and  finished,  with  heads  of  approved 
shape,  full,  and  of  equal  size.  They  shall  be  central  on  the  shank  and  shall  grip 
the  assembled  pieces  firmly.  Re-cupping  and  calking  will  not  be  allowed. 
Loose,  burned,  or  otherwise  defective  rivets  shall  be  cut  out  and  replaced  In 
cutting  out  rivets,  great  care  shall  be  taken  not  to  injure  the  adjoining  metal. 
If  necessary,  they  shall  be  drilled  out. 

36.  Field  Bolts.     Wherever  bolts  are  used  in  place  of  rivets  which  trans- 
mit shear,  such  bolts  must  have  a  driving  fit.    A  washer  not  less  than  J  in.  thick 
shall  be  used  under  the  nut. 

37.  Members  to  be  Straight.     The  several  pieces  forming  one  built  member 
shall  be  straight  and  shall  fit  closely  together,  and  finished  members  shall  be 
free  from  twists,  bends,  or  open  joints. 


STEEL  CONSTRUCTION  369 

38.  Finish  of  Joints.    Abutting  joints  shall-  be  cut  or  dressed  true  and 
straight  and  fitted  closely  together,  especially  where  open  to  view.    In  compres- 
sion joints  depending  on  contact  bearing/ the  surfaces  shall  be  truly  faced,  so  as 
to  have  even  bearings  after  they  are  riveted  up  complete  and  when  perfectly 
aligned. 

39.  Eyebars.    Eyebars  shall  be  straight  and  true  to  size,  and  shall  be  free 
from  twists,  folds  in  the  neck  or  head,  or  any  other  defect.    Heads  shall  be 
made  by  upsetting,  rolling,  or  forging.    Welding  will  not  be  allowed.   The  form 
of  the  heads  will  be  determined  by  the  dies  in  use  at  the  works  where  the  eyebars 
are  made,  if  satisfactory  to  the  engineer,  but  the  manufacturer  shall  guarantee 
the  bars  to  break  in  the  body  with  a  silky  fracture,  when  tested  to  rupture.    The 
thickness  of  the  head  and  neck  shall  not  vary  more  tnan  &  in.  from  the  thickness 
of  the  bar. 

40.  Boring  Eyebars.    Before ,  boring,  each  eyebar  shall  be  perfectly  an- 
nealed and  carefully  straightened.'   Pin  holes  shall  be  in  the  center  line  of 
bars  and  in  the  center  of  heads..   Bars  of  the  same  length  shall  be  .bored  so 
accurately  that,  when  placed  together,  pins  ^?  in.  .smaller  in  diameter  than  the 
pin  holes  can  be  passed  through  the- holes  at  .both  ends  of  the  bars  at  the  same 
time. 

41.  Pin  Holes.    Pin. holes  shall  be -bored  true   to   'gages,  smooth  and 
straight;  at  right  angles  to  the1  axis  of  the  member,  and  parallel  to  each  other, 
unless  otherwise  called  for.  •  Wherever  possible,  the  boring  shall  be  done.  afteY 
the  member  is  riveted  up. 

42.  Variation  in  Pin.  Holes,    The  distance  from  center  to  .center  of  pin 
holes  shall  be  correct  within  ^j  in.,  and  the  diameter  of  the  hole  not  more  than 
B"&  in.  larger  than  that  of  the  pin,  for  pins  UD  to  5  in.  diameter,  and  •&  in,  for 
larger  pins. 

43.  Pins  and  Rollers.  -  Pins  and  rollers  shall  be  turned  accurately  .to 
gages,  and  shall  be  straight,  smooth,  and  entirely  free  from  flaws. 

44-    Pilot  Nuts.    At  least  one  pilot  and  driving  nut  shall  be  furnished  for 
each  size  of  pin  for  each  structure. 

45.  Screw  Threads.    Screw  threads  shall  make  tight  fits  in  the  nuts,  and 
shall  be  United  States  standard,  except  for  diameters  greater  than  If  in.,  when 
they  shall  be  made. with  six  threads  per  inch. 

46.  Annealing.    Steel,  except  in  minor  details,  which  has  been  partially 
heated  shall  be  properly  annealed. 

47.  Steel  Castings.    All  steel  castings  shall  be  annealed. 

48.  Welds.    Welds  in  steel  will  not  be  allowed. 

49.  Bed  Plates.    Expansion  bed  plates  shall  be  planed  true  and  smooth. 
Cast  wall  plates  shall  i>e  planed  at  top  and  bottom.    The  cut  of  the  planing 
tool  shall  correspond  with  the  direction  of  expansion. 

60.  Shipping  Details.    Pins,  nuts,  bolts,  rivets,  and  other  small  details 
shall  be  boxed  of  crated. 

61.  Weight.    The  weight  of  every  piece  and  box*  shall  be  marked  on  it  in 
plain  figures. 

Curved  framing,  hoppers,  bins,  and  other  complicated  work 
shall  be  assembled  and  fitted  in  the  shop. 


370  STEEL  CONSTRUCTION 

\ 

Cast  Iron.  The  ends  of  cast-iron  columns  and  the  tops  of  base 
plates  and  pedestals  must  be  finished  exactly  at  right  angles  to  the 
vertical  axis  of  the  column. 

The  thickness  of  metal  in  cast-iron  columns  shall  be  not  less  at 
any  point  than,  that  marked  on  the  design  drawings.  The  inside 
must  be  concentric  with  the  outside.  Shifting  of  the  core  more  than 
£  inch  will  cause  rejection.  At  least  three  holes  shall  be  drilled  in 
each  column  to  test  the  thickness  of  metal. 

Fins,  chaplets,  and  other  irregularities  shall  be  removed  by 
chipping,  leaving  neatly-finished  surfaces.  No  holes  shall  be  filled 
with  cement  or  other  substance  without  permission  from  the  Archi- 
tect. 

The  best  practice  shall  be  followed  in  reference  to  the  quality 
of  sand,  molding,  and  the  stripping  of  molds  from  castings. 

Painting*  The  material  shall  be  painted  one  coat  of  red  lead 
paint  at  the  shop  and  one  coat  of  graphite  paint  after  erection. 
The  painting  shall  be  done  in  accordance  with  paragraphs  52  to  58 
of  Schneider's  Specifications. 

5%.  Shop  Painting.  Steelwork,  before  leaving  the  shop,  shall  be  thor- 
oughly cleaned  and  given  one  good  coating  of  pure  linseed  oil,  or  such  paint  as 
may  be  called  for,  well  worked  into  all  joints  and  open  spaces. 

53.  In  riveted  work,  the  surfaces  coming  in  contact  shall  be  painted 
before  being  riveted  together. 

54'  Pieces  and  parts  which  are  not  accessible  for  painting  after  erection 
shall  have  two  coats  of  paint  before  leaving  the  shop. 

55.  Steelwork  to  be  entirely  embedded  in  concrete  shall  not  be  painted. 

56.  Painting  shall  be  done  only  when  the  surface  of  the  metal  is  perfectly 
dry.    It. shall  not  b«  done  in  wet  or  freezing  weather,  unless  protected  under 
cover. 

57.  Machine-finished  surfaces  shall  be  coated  with  white  lead  and  tallow 
before  shipment,  or  before  being  put  out  into  the  open  air. 

58.  Field  Painting.    After  the  structure  is  erected,  the  metal  work  shall 
be  painted  thoroughly  and  evenly  with  an  additional  coat  of  paint,  mixed  wi!h 
pure  linseed  oil,  of  such  quality  and  color  as  may  be  selected,    The  field  paint 
shall  be  of  different  color  from  the  shop  paint. 

Inspection  and  Testing.  The  inspection  and  testing  will  be 
done  by  the  Architect  or  his  representative.  The  contractor  shall 
furnish  the  facilities  for  inspecting  and  testing  and  be  governed  by 
all  of  the  provisions  contained  in  paragraphs  59  to  64  of  Schneider's 
Specifications. 

59.  The  manufacturer  shall  furnish  all  facilities  for  inspecting  and  testing 
the  weight,  quality  of  material,  and  workmanship.    He  shall  furnish  a  suitable 


STEEL  CONSTRUCTION  371 

testing  machine  for  testing  the  specimens,  as  well  as  prepare  the  pieces  for  the 
machine,  free  of  cost. 

00.  When  an  inspector  is  furnished  by  the  purchaser,  he  shall  have  full 
it  all  times  to  all  parts  of  the  works  where  material  under  his  inspection 
is  manufactured. 

f>'l.  The  purchaser*  shall  be  furnished  with  complete  copies  of  mill  orders, 
and  no  material  shall  bo  rolled  and  no  work  done  before  he  has  been  notified  as 
to  where  the  orders  have  boon  placed,  so  that  he  wiay  arrange  for  the  inspection. 

62.  The  purchaser  shall  also  be  furnished  with  complete  shop  plans,  and 
must  be  notified  well  in  advance  of  the  start  of  the  work  in  the  shop,  in  order 
that  he  may  have  an  inspector  on  hand  to  inspect  the  material  and  workmanship. 

63.  Complete  copies  of  shipping  invoices  shall  be  furnished  to  the  pur- 
chaser with  each  shipment. 

64-  If  the  inspector,  through  an  oversight  or  otherwise,  has  accepted 
material  or  work  which  is  defective  or  contrary  to  the  specifications,  this  material, 
no  matter  in  what  stage  of  completion,  may  be  rejected  by  the  purchaser. 

Erection.  Conditions  at  the  Site.  (To  be  changed  to  suit  the 
case).  The  site  of  the  building  cannot  be  given  over  to  the  con- 
tractor for  his  exclusive  use.  He  must  conduct  his  work  as  directed 
by  the  Architect,  and  in  harmony  with  the  other  contractors  working 
on  the  building  at  the  same  time. 

There  is  no  storage  space  on  or  adjacent  to  the  building  site  so 
the  contractor  must  deliver  the  material  as  needed  for  erection, 
except  arrangements  may  be  made  from  time  to  time  for  the  tem- 
porary storage  of  small  quantities  of  material.  He  shall  provide 
elsewhere  such  storage  space  as  he  may  need. 

Construction  Equipment.  The  contractor  shall  furnish  all 
equipment  required  for  his  operations.  The  equipment  shall  be  ade- 
quate for  its  purpose,  and  must  have  ample  capacity  to  carry  on  the 
work  quickly  and  safely.  The  Architect  shall  have  authority  to  order 
changes  in  equipment. if,  in  his  judgment,  it  is  not  adequate  or  safe. 

Storing.  Stored  materials  must  be  placed  on  skids  and  not  on 
the  ground.  They  must  be  piled  and  blocked  up  so  that  they  will 
not  become  bent  or  otherwise  injured. 

Unpainted  material  shall  not  be  so  stored  in  the  open.  The 
materials  shall  be  handled  with  cranes  or  derricks  as  far  as  prac- 
ticable. They  must  not  be  dumped  off  of  cars  or  wagons  nor  in  any 
other  way  treated  in  a  manner  likely  to  cause  injury. 

Erecting  Steel  and  Iron  Work.  The  structural  steel  and  iron 
work  shall  be  erected  as  rapidly  as  the  progress  of  the  other  work 
(particularly  foundations  and  walls)  will  permit. 


372  STEEL  CONSTRUCTION 

Setting  Plates  and  Grouting.  Base  plates,  bearing  plates,  and 
ends  of  girders  which  require  to  be  grouted,  shall  be  supported 
exactly  at  proper  level  by  means  of  steel  wedges.  The  grout  will 
be  furnished  and  poured  by  the  mason  contractor.  - 

Plumbing,  Leveling,  Bracing.  The  structural  steel  and  iron 
work  shall  be  set  accurately  to  the  lines  and  levels  established  for 
the  building,  as  shown  on  the  drawings.  Particular  care  shall  be 
taken  to  have  the  work  plumb  and  level  before  riveting. 

Necessary  bracing  shall  be  provided  for  this  purpose,  and  for 
resisting  stresses  due  to  derricks  and  other  erection  equipment  and 
erection  operations. 

Elevator  shafts  shall  be  plumbed  from  top  to  bottom  with 
piano  wire  and  must  be  left  perfectly  plumb. 

Temporary  Bolts.  The  members  shall  be  connected  tempor- 
arily with  sufficient  bolts  to  insure  the  safety  of  the  structure  until 
it  is  riveted.  Not  less  than  one-third  the  holes  shall  be  bolted. 

Riveting.  All  field  connections  shall  be  riveted  unless  other- 
wise ordered.  The  riveting  shall  follow  as  closely  as  practicable 
after  erection.  The  connecting  members  shall  be  drawn  up  tight 
with  bolts  before  riveting.  Rivets  generally  shall  be  driven  with 
pneumatic  hammers. 

The  rivets  must  be  of  proper  length  to  form  full  heads.  Rivets 
must  be  tight,  with  full  concentric  heads.  Defective  rivets  must  be 
cut  out  and  re-driven.  No  re-cupping  or  calking  will  be  allowed. 

Permanent  Bolts.  When  bolts  are  used  for  permanent  connec- 
tions, washers  shall  be  placed  under  the  nuts,  the  nuts  drawn  tight, 
and  the  threads  checked.  In  such  cases,  bolts  must  be  used  which 
are  provided  for  that  purpose,  and  not  ordinary  machine  bolts. 

Connections  to  cast  iron  shall  be  bolted. 

Removal  of  Equipment  and  Rubbish.  The  contractor  shall 
remove  the  construction  equipment  as  rapidly  as  its  service  is  com- 
pleted and  shall  remove  all  rubbish  from  day  to  day. 

Immediately  after  final  acceptance  of  the  work,  the  contractor 
shall  remove  all  his  equipment  and  property  and  shall  remove  all 
rubbish  resulting  from  his  operations. 


INDEX 


INDEX 


Angle  collections —  120 

Angles - 29 

B 

Beam  _ - 75 

restrained 75 

simple 75 

Beam  box  girders _ ___ __.  159 

Beam  design _ _ _.  76 

deflection . __ __77,  80 

flexure 77 

modulus  of  elasticity 80 

shear 77,79 

Beam? 

anchors .. .. 134 

beam  design,  theory  of _ __  76 

bearings — 130 

classification _  75 

connection  of  beams  to  beams 120 

angle  connections ._  120 

special  connections. ._ _ 124 

connections  of  beams  to  columns. __ 124 

combination  connections 127 

seat  connections   _ 124 

web  connections _ _ 126 

construction  details , 120 

definitions _ 75 

design  of,  practical  illustration _ 309 

details  of  construction 120 

lateral  support 112 

load  effects,  calculation  of_. 80 

miscellaneous  details  __ 134 

practical  applications __ 113 

resistance,  calculation  of 97 

sections 76 

separators 127 

strength  of,  tables. 100-107 

tie  rods 129 

Bearing  _ __ __ 64 

Bearing  plates _ 130,  165 

Bending  moment 76 


2  INDEX 

PAGE 

Bending  moment  diagram _ - 262 

restrained  beam 262 

unit  bracing 263 

Bessemer  process  ._ . 13 

Bethlehem  columns 189,  196-209 

tables - 196 

Bolts 71 

bolts  in  tension .j 72 

machine  bolts _ . . 72 

turned  bolts 72 

Breaking  load 47 

C 

Cantilevers 1 18 

Cast  iron 51 

Cast-iron  columns 225 

column  sections. . 226 

details  of 232 

method  of  design __ 226 

tables • 229 

Cast-iron  pedestals. 220,  3 1 9 

Cement  as  a  rust  preventive 339 

Center  of  gravity  (C.  G.) 35 

Channel  columns,  tables 210-215 

Channels . 28 

Chemical  composition  of  steel 45 

Chimney  supports 327 

Chord  stress  in  girders 135 

Column  bases 218,  319 

cast-iron  plates 220 

flat  plates 219 

steel  grillage 224 

Column  loads  and  their  effects _ _ 173 

computation  of  loads 173 

concentric  loads 174 

eccentric  loads 174,  315 

illustration 175 

Column  sections 183,  226,  318 

area. 181. 

distance  from  neutral  axis  to  extreme  fiber 181 

moments  of  inertia 182 

properties  of 181 

radius  of  gyration 182 

Columns 1 73 

Bethlehem 189 

details  of ;  216 

brackets 218 

connections .» * 218 

lacing 217 


INDEX  3 

PAGE 

Columns 

details  of 

riveting . 217 

splices 216 

location  of - 308 

practical  illustration 313 

steel _ --. -.  173 

strength  of 179,196-215,229 

formulas. 179,  189,229 

unit  stress 179,  189,  190.  192,  194 

tables -. 196-209 

wind  bracing,  stresses  in 266 

Connections 120 

beams  to  beams 120 

beams  to  column 124 

girders  to  columns 166 

D 

Deflection 77,  80,  109 

Details  of  construction '. 120,  134,  166,  231,  261,  263 

Dimensioning  drawings _ 329 

E 

Eccentric  loads  on  columns 174,  227,  315 

Elastic  limit 47 

Equilibrium . 3 

Erection . 371 

F 

Factor  of  safety 7 

Fire,  protection  from 339 

Fireproof  floor  construction 301 ,  306 

Fireproof  materials _. _.  342 

Fireproofing 294,  339 

requirements,  Chicago  Building  Ordinances 347 

Floor  construction,  fireproof 301,  306 

Floor  framing,  panel  of . 113,  303,  305,  306 

Friction  ..  .67 


G 
Girders  (see  Riveted  girders) 134 

H 

H-sections _  _  1 33 

Hangers  (see  Tension  members) 233 


4  INDEX 

PAGE 
I 

I-beam  with  flange  plates _.  158 

I-beams __ _ 25 

Inspection .__ _ 370 

Inspection  and  tests __ ___ ... 48 

J 
Joist 75,  81 

L 

Lateral  support 172 

Lintel.. 75,  116 

Load  effects,  calculation  of _ 137 

combined  loads  _ 89 

concentrated  loads _ _ 85 

cantilever  beams 86 

simple  beam 85 

simple  beams  on  two  supports  and  projecting  at  both  ends 86 

typical  loadings 93 

beam  with  two  or  more  loadings __     96 

moving  loads 96 

simple  lo'ads _ 93 

tabular  data__ 93 

uniformly  distributed  loads 80 

cantilever  beam 81 

combination  simple  and  cantilever  beam 82 

joists 81 

Loads. 295,  351,  356 

dead....1 295,  303,  304,  309 

live J...297,  299,  314 

M 

Manufacture  of  steel  _._ 9 

iron  ore  to  pig  iron _ 9 

pig  iron 10 

process  of  smelting.  _ 9 

pig  iron  to  steel . 11 

acid  open-hearth  process 14 

basic  open-hearth  process 16 

bessemer  process. 13 

rolling  the  ingots 18 

blooming ...  19 

plate  rolls 22 

roughing  and  finishing  rolls... _ 19 

Manufacture  of  steel  sections 44 

Masonry 52 

Masonry  supports _- 327 


INDEX  5 

PAQB 

Material,  quality  of 42 

miscellaneous  sections 34 

plates _ 32 

tees -_ _ 31 

Mill  and  stock  orders _ _. 40 

Miscellaneous  properties _ _ 39 

Moment  of  inertia  (I) ., ..36,  140, 182 

N                   7 
Neutral  axis 181 

O 
Open-hearth  process 14 

P 

Paint - ......335,363 

Painting _ ..335,  370 

Pig  iron __ 10 

Plate  box  girders.. ._- 160 

Plate  girder  (see  Riveted  girder) _ 134 

Plates.... - — 32 

Practical  design  of  sixteen-story  fireproof  hotel ; 269 

column  pedestals _  319 

column  specifications 313 

dimensioning  drawings 329 

fireproof  specifications _ 294 

floor  construction,  type  of _ 301 

framing  specifications * _ 306 

loads. _ _ 295 

miscellaneo  is  features __ _.  327 

wind  bracing __ 322 

Price  basis  ... 40 

Protection  (see  Rust,  Painting,  and  Fireproofing) 333 

Punching _ __     62 

Q 

Quality  of  materials _  352 

cast-iron 361 

paint. 363 

steel 359 

R 

Radius  of  gyration  (r) 38,  182,  228 

Railway  bridge  grade  steel _ _ 46 

Reaming _ 62 

Reduction  of  area 48 

Reference  books 5 


6  INDEX 

PAGE 

Resistance,  calculation  of 97 

deflection 109 

deflection  formulas 109 

safe  span  length 110 

lateral  support 112 

resisting  moment 97 

application  of  tables  to  concentrated  loads 99 

section  modulus 98 

tabular  values  for 98 

shearing  resistance  _, 108 

Resisting  moment 76,  77,  97,  135 

determination  of 135 

chord  stress  method 135 

moment  of  inertia  method 135 

Restrained  beam 75 

Rivet  tables 67 

Rivets 52 

bearing 64 

driving 58 

hand  riveting 62 

pneumatic  hammer 61 

riveting  machines  in  shop 60 

friction 67 

function  of 63 

investigation  of  riveted  joints 67 

length  of 73 

ordinary  sizes 52 

punching  and  reaming 62 

rivet  heads 56 

button  head 57 

flattened  and  countersunk  head 57 

manufacture 57 

shear 65 

spacing 53 

clearance 55 

edge  distance 55 

gage 54 

pitch 54 

tension 67 

Riveted  girder J 134 

beam  box  girder 159 

crane  girder .__  164 

design,  tKeory  of 135 

girder  supporting  a  column 162 

I-beam  with  flange  plates 158 

plate  box  girder 160 

plate  girder .-  138 

plate  girder  lintel 164 

practical  applications, .._  ^ _ - 162 


INDEX  7 

I'AOB 

Riveted  girder 

roof  girder 164 

unsymmetrical  sections 160 

Riveted  girder  design 135 

depth 138 

economy 138 

flange  section 141 

width  of  flange  plates. 143 

with  flange  plates 142 

without  flange  plates 141 

length  of  flange  plates _  _  _ 144 

graphical  solution  for  concentrated  loads 145 

graphical  solution  for  uniformly  distributed  loads 145 

moment  of  inertia  required ___ 140 

rivets  connecting  flange  angles  to  web  _.. r 149 

number  of  rivets 149 

rivet  spacing  computed  from  web  bearing 152 

rivet  spacing  in  flanges 150 

riveting  for  cover  plates 150 

spacing  when  load  transmitted  through  flange  rivets  into  web 152 

tables  and  diagrams 154 

thickness  of  web 139 

shearing  value  of  web  plates 140 

web  stiffeners 146 

intermediate  stiffeners 148 

stiffeners  at  loaded  points 146 

Riveted  girder  details. 165 

connections  to  columns 166 

bracket  connection •_ 167 

web  angle  connection 166 

end  bearings 165 

lateral  support 172 

splices 168 

Riveted  joints 67 

Riveters 59 

Riveting  in  girders 149 

Rolling  steel 18 

Rust 333 

cement  as  a  preventive 339 

paint  as  a  preventive 335 

S 

Section  modulus  (QJ - 39 

Section,  steel — adaptability  and  use _  23 

angles. _ 29 

channels 28 

Hrsection 33 


8  INDEX 

PAGE 

Section,  steel — adaptability  and  use 

I-beams 25 

Bethlehem  sections 26 

Carnegie  sections 26 

efficiency  of  minimum  sections 27 

special  sections , 25 

standard  sections 25 

Shear 65,  77,  79,  108 

Simple  beam 75,  81,  85 

Smelting 9 

Span 75 

Spandrel = 75 

Spandrel  girders,  practical  illustration 310,  323,  328 

Specifications 349 

example  of _  353 

general  characteristics 350 

purpose  of 349 

details  of  construction 363 

erection 371 

example  of 353 

general  conditions 353 

inspection  and  testing 370 

loads. 356 

outline 350 

painting 370 

quality  of  materials '_  359 

unit  stresses 357 

workmanship 368 

Standard  specifications 350 

bending  requirements 44 

chemical  analysis 43 

elongation  and  fracture 44 

process  of  manufacture 43 

range  of  application 43 

rivet  steel  strength 44 

tensile  strength 43 

Strength  of  columns  (see  Tables) 189 

Structural  steel.  „_ _ 9 

manufacture  of _.       9 

maximum  allowable  stresses  on __ 51 

procedure  in  furnishing 8 

reliability  of ___ 42 

T 
Tables 

beams,  strength  of _ 100-107 

gages  for  angles _ __ 54 

moments  of  inertia  of  I-beams  with  holes  in  flanges  _ _ 159 

safe  loads  for  round  cast-iron  columns 229 


INDEX  9 

PAOB 

Tables 

safe  loads  on  Bethlehem  columns 196-209 

safe  loads  on  channel  columns 210-215 

typical  loadings,  reactions  and  bending  moments  for 94-95 

unit  stress  in  compression 194 

unit  stress  in  compression  in  columns .190-193 

Tables,  use  of - 194 

Tank  support 118 

Tees -     31 

Tension  members 233 

connection  details 237 

definition  and  theory 233 

axial  tension 233 

tension  due  to  eccentricity 234 

not  area 236 

sections 235 

Trsting . 370 

U 

Unit  stresses.. 50,  51,  351,  357 

columns 179,  190,  192 

tension _.  234 

zees - 30 

w 

Weights  of  materials 295 

Weight,  variation  in 41 

Wind ....322,329 

Wind  bracing 239,  322 

combined  wind  and  gravity  stresses  in  girders 262 

framework,  systems  of  rectangular  framework 246 

axial  stresses 253 

triangular  framework 243 

horizontal  pressures 239,  322 

moment  diagram  for  a  restrained  beam 262 

paths  of  stress _ 240 

wind  bracing  girders,  design  of _  .255,  323 

end  connections  for  I-beam  girders .261,  323 

end  connections  for  riveted  girders 255,  324 

wind  stresses  on  columns,  effect  of 266,  322,  326 

Workmanship 368 

Y 
Yield  point 47 

Yield  point  and  factor  of  safety. 48 


Zees 30 


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